But what should I be expecting? How much trouble am I in?
If you graduated with $134,181 in loans at a rate of 9.3% you'd expect a repayment amount of $1,722/month for 10 years. If you make $70,000/year you'd have ~$2,617 after your loan payments each month, and if the $1,800 monthly living expense you mention is sustainable during loan repayment then you'd have an excess $817 each month.
As for trouble, one common mistake that many people make after landing a job after school is increasing their cost of living, they want a nicer car/apartment/furniture and spend more going out for food/drinks. The best thing you can do is keep in mind that every $1 you spend on something other than debt costs you an extra 9.3% compounding month after month.
What advice or resources would you recommend for handling finances like these going forwards?
I suggest focusing on living frugally, save up a small emergency fund (maybe just 1-2 months expenses) with your excess each month and after that start applying all extra towards the loans. Don't forego company 401k match, but I would skip other investments during aggressive repayment.
A proper written/electronic budget helps a lot of people, I recommend some form of a zero-based budget which is characterized by every dollar being given a purpose. Not just tracking spending like with Mint, but proactively deciding how each dollar will be spent as best as possible.
Extra income from a side job would be great and could really speed up the repayment, again, use the 9.3% interest as motivation to do whatever is necessary. An extra $800/month shaves ~50 months off your repayment period. Also, as your pay increases over time you can put even more towards these loans each month. This is also a great mindset to have with retirement saving, if you increase your retirement contributions with each pay-raise rather than increasing your cost of living you can speed up your retirement saving very quickly.
Also a note about repayment, while I mentioned the standard repayment amount as if you had one loan at 9.3% in actuality you have multiple loans at different rates. If you can consolidate to a lower rate, that could be fantastic, if not I suggest you make minimum payments on all loans, then any extra you can afford will go to the loan with the highest interest rate. Some people advocate starting with the smallest balance, but that isn't the most efficient (at least mathematically, the psychological benefit for some can make it preferable).