The IRS wants you to file taxes
This has me spooked, because lots of people pretend to be the IRS so they can scam you. They tend to use telephone or online as the first method of contact (IRS uses postal mail only). They also like to be paid in goofy ways like Western Union, iTunes gift card, or wire transfers to funny bank accounts.
Obviously, scammers don't want you interacting with the real IRS because they won't be able to fool you if the real IRS is telling you the truth.
IRS considers each tax year to be a separate thing. They want you to file your Form 1040 personal taxes for each year. (Or use an acceptable equivalent such as e-"file" with H&R Block, Turbotax, etc.). *
Your tax troubles surely apply to previous tax years. They definitely want you to file taxes this year!!!
IRS doesn't care about your single-member LLC
Right now, when you make money in your business, the IRS just considers that as personal income, and you are allowed to deduct the real costs of the business. You report it on your personal 1040.
OK, form an LLC where you are the only member (owner), and take the default tax treatment. What happens now? Absolutely nothing. You still report the business income and expenses on your personal 1040. The IRS doesn't care about the LLC, it calls it a "disregarded entity".
The IRS doesn't know about the LLC
The IRS doesn't have anything to do with LLCs. When you form an LLC, you are dealing with your own state. You pay the fees to the state etc.
The only thing you deal with the IRS on, when forming an LLC, is if you need an "EIN" or "Employer Identification Number". Which you will probably need if you want to open a bank account for the business, or seek credit for the business e.g. Getting net-30 terms with suppliers. Obviously if you ask for an EIN, the IRS will know you have it, but they won't care.
The IRS will like the LLC, in any case
If the dispute with the IRS is over how much money you actually made (i.e. If the IRS is accusing you of hiding cash income), then the IRS will approve of the LLC.
In a properly run business, you never "take money out of the till" for expenses. Every single raw dollar is deposited direct into the company bank account. Every single expense you pay is paid out of the company account. This acts like a journal, but it's kept by an independent third party: the bank. The expenses are much easier to prove because there's a debit card charge to Aveda, a check to OfficeMax, etc. etc.
Making it very easy for outsiders to audit your day by day business. Not just the IRS; imagine you dedided to sell your business and needed to prove your income to the buyer. There it is, in years of bank statements.
A journal is still better, and a journal that matches up everyday to the bank deposits, is rock solid proof that you are making a real effort to keep accurate books. If you had that, the IRS could not easily claim that you were hiding income.
* If you don't file, the IRS will try to figure out what you owe, i.e. "Do your taxes for you". This is provisional; you can override it by actually filing your taxes. IRS would still prefer you actually file. In your case in particular, "IRS doing your taxes" presumes all your income has been reported on W-2s or 1099 forms: As a self-employed cosmetologist, a lot of your income is cash and it's all on you to tally and report that. You should keep a contemporaneous (written down when it happens) journal of all your income, payment method and expenses. Some say "how would IRS know that I just got $50 cash? They can't know that, so I just won't log it! Haha!" And that blows up in their face.