When considering such a major life decision, with such high potential costs and high potential rewards, I encourage you to consider multiple different potential options. Even if loans were available, they might not be the best option. Less debt and an engineering degree is better than more debt and an engineering degree, both of which are likely better than your current debt and no engineering degree.
I encourage you to consider: revisit your aid (which is not just loans), cut expenses, consider alternative aid sources, use your engineering student status to get a better paying job (including more profitable summer employment), check for methods to cut down the cost of your degree, and double-check your plans to make sure you have a long-term plan that makes sense.
Talk to a Financial Aid Councillor at Your School About More Than Just Loans
The first issue, raised in the comments, is whether or not you are getting appropriate financial aid. This does not just mean loans, it includes grants and other forms of assistance.
You should be getting in-state tuition, and by searching the tuition of UNC I believe you are. But for future readers, you should make sure you are getting in-state rates, and it not there are options to return to a state where you would get in-state tuition rates, or look into the possibility of pausing your study for one year until you meet in-state funding requirements.
You should also ensure your FAFSA information is correct, including your income, family situation (whether or not you are an independent study, as it sounds like you probably are), etc. This effects how many grants you get, and if you are independent this changes maximum federal loan amounts (see website for details).
While you don't say what your pay is, the fact that you are working two jobs and having trouble making ends-meet suggests either that you have a spending issue, or that your jobs pay sucks, and possibly both. I've been in both situations, and there are methods for dealing with both.
If your spending is not very carefully controlled, that's a big issue. I won't try to rehash all the personal finance advice about this, but I will just warn that when you are desperate and you know there isn't enough money even if you spend perfectly, there is a strong tendency to just give up and not even try because what's the point? Learned helplessness is hell, but it can be overcome with effort and tightly holding on to any glimmer of hope you find to do better each day.
Better Jobs Even Before You Finish School
If you are in a field like engineering or computing (and some other fields, though I am less personally familiar with the current employment climate in those), there are usually companies who want to hire you as a paid intern or part-time employee in the hopes of getting you when you graduate. Those last two semesters of undergrad are a technicality to employers, they know it doesn't really change your skill set much. Many companies are actually more interesting in hiring someone on who hasn't finished the degree yet than getting someone recently post-degree, because they can get you cheaper and learn if this is a good match before they have to take the big risk of full-time hiring.
You need to use this system to your advantage. Its hard when you feel destitute, but talk with career councilors in your school, your department advisor, and/or main administrative staff in your main academic department. Make sure you are on the right mailing lists to see the job offers (many schools require you to subscribe to one because at a school like UNC it easily gets way too much traffic each day). You need field-relevant experience, not just to finish the degree, but to be able to really open up your job opportunities and earning potential.
Do not be shy about directly calling/emailing a contact who reaches out to your school looking for "recent graduates", and especially any mention of flexibility on early start for those who are almost finished. You can say you are in your final year (you are), and even ask if they are open to working around a light school schedule while you finish up. Most can end up to be "no", but it doesn't matter - the recruiting contacts want to hire people, so just reaching out early means you can follow up later once you get your degree and finances sorted out and you will have an even easier time getting that opportunity.
High-paying Summer Internships
In technology and engineering, the importance of summer internships cannot be understated, especially as you are now technically at the end of your degree. In engineering and tech fields, internships pay - often very well. Don't worry about it being the job of your dreams. Depending on your set of skills, apply to insurance companies, IT departments in hospitals and banks (even if you thought your coding skills in engineering were minimal), and of course any paying position that might be more directly in your field of interest. Consider ones outside your immediate area or even the more national internships from the bigger name companies, where possible.
It is not at all uncommon for tech and engineering internships for undergraduate students to pay $15-$25+ per hour, even where most non-degree jobs might only pay $8 (and I've seen as high as $40 per hour+ in the high cost of living markets, depending on your skill set). I know many people who were paid more as a student intern than they were previously paid as a full-time professional employee.
Check for Cheaper Class Credit Options
Many schools - including UNC - charge different tuition for distance learning and satellite campuses, and often also offer University-approved online classes. While this is not always a possibility for every student, you should consider the options.
It could be that one of the final classes you need towards your degree can be taken at one of these other options, with reduced tuition. This is not always possible with all courses, but is certainly true if you have any of those general education requirements to knock out.
Also consider if any of those final requirements have test-out options, such as CLEP test alternatives. Again, not always available, but sometimes you can get class credit for a general education class for
Finally, make sure you aren't paying unnecessarily for text books, once you do get the money for tuition. You can sometimes get hand-me-down copies, rent ebooks or physical books from online companies, creative searches for PDF copies, get your book from off-campus local stores, etc. It isn't tuition, but money is money.
Attend Part-Time While Working
Look into the option of being a half-time student, which is usually 6-8 credit hours, if you can't afford full-time tuition. There is generally a greatly reduced rate, you still qualify for aid programs, and you are still working towards the degree - so you still get access to student resources like internships and job listings that may not be publicly posted.
Inquire About Scholarships and School Emergency Assistance
While this varies hugely by institution, make sure you check into scholarships you can apply to (even if they are just a few hundred bucks, it helps a lot) in your school (I don't believe the big online searches help, ask the school - but YMMV). Also inquire about any sort of possible help the school provides to students who've had life emergencies, such as your medical issues. Many have programs that are not advertised, designed to help students finish their degree and recover from personal hard times. It's worth the inquiry if you are willing to ask. Any little bit of assistance can help.
Don't be afraid to talk with an institution's mental health councilors either, who can help you deal with the psychological difficulty of your situation as well as often being able to connect you to other potential support resources. The pressure can take its tole, and you'll have better long-term opportunities if you build up your support network and options.
Student Loan Forbearance While In School
If you are trying to save up every last dollar for tuition to finish the degree, but you have to pay loans now, call up the provider to ask about temporary delays on your student loan payments. Many have time-limited hardship allowances, and between the medical bills, low income, and returning to school, they may be willing to give you a few months break until you get back to school and the in-school provisions kick in.
Skip a Semester If Necessary To Save Money
If you can only raise enough for one semester, then need to skip a semester to build up more funds, that happens, it's OK. Be strategic, and check on loan forbearance. Usually being out for one semester is allowed by student loan companies before you owe them payment, and if you re-enroll you don't have to start making payments yet.
Double-check on Credit Expiration and Degree Requirements
Make sure you talk to someone who knows what they are talking about, especially in terms of credit expiration. Policies vary, and sometimes an advisor is able to put in a special request to waive you through some of these issues. Academia is heavily, heavily reliant on developing a good relationship and clear communication with an advisor who is willing to work with you to achieve your goals. Written policies are sometimes very firm, and sometimes all you have to do is ask the right person and poof, suddenly the rules change.
It's a weird system, but don't be afraid to explain your situation and ask what can be done. Don't assume a written policy is 100% ironclad - sometimes it is, but it often isn't.
Inquire About Other Government and Community-based Assistance
Being destitute is awful, and having to ask for help can feel terrible in it's own way, but doing what you have to do to have a better future can mean pushing through and being willing to ask for help. This can mean asking parents and close family if they can contribute to help you finish your degree, but this also means checking with your local community programs to see if you qualify for anything. Many communities have food pantries and related programs that will help you even if you don't qualify for something like SNAP (aka food stamps), because they know times can get hard for anyone and they want you to spend what little money you have on building a better life.
Your university may even run a food pantry for students in need - use it. Get what assistance you can, minimize spending in any way you can manage, put all the money towards doing what you need to do to get to a better place. It's even nicely reciprocal - once you work through your hard times and get things on track, you can return the favor and help give back to programs like the ones that helped you.
Make Sure Your Long-Term Goal Makes Sense
Finally, this is all predicated on pulling out all the stops to finish your degree. But this assumes that this is a good plan. Not all degrees are helpful for all people in all areas of the country. Do your own research to make sure you aren't throwing good money after bad, and are pursuing a goal that will make sense for you and what you want.
The cost of a degree keeps going up, but it remains true that many sets of skills and degree-holding candidates are in demand and can command high salaries that blow away the cost of college in comparison. If you actually have a good chance of going from struggling to make $8/hour to making $50k-90k a year, based on your developed skills, experience, and professional network, then reasonable student loan debt is a worthy investment. If, on the other hand, you wrack up tens of thousands of more dollars in debt just to say you did and still have to work the same kinds of jobs, that's not really much of an investment at all.
Good luck on your journey, and best wishes towards better days - regardless of what path you choose.