Refinancing will be a huge weight off your shoulders! I was in a very similar boat. Graduated in 2012. About $80k total in loans, 2/3 of which were private with variable interest rates. 6 months after I graduated the payments kicked in at $1100 a month. Since income based repayment's only an option for federal, even after that reduced the fed portion of the payment almost to 0, I was still paying out $800 a month. By 2014 those variable interest rates were fucking me hard at 12.5%. Every time I tried to refinance I was told I couldn't because I still owed too much.

After my uncle died in 2017, my parents were left his house and told me that once they paid off their credit cards, they'd help me pay off my loans with the rest. It should have been most, if not all of the private at the least. My uncle had stopped taking care of himself before he died and the house was in disrepair and infested with bedbugs. After all those problems were dealt with and a few other remaining estate debts settled, what was left was maybe 25% of what we originally thought there would be.

Still, my parents gave me what they could and that $10k was just enough to pay off one of the high interest rate loans (may have been up to 13% by this point) which finally brought my balance down enough to refinance. Was sure to do a fixed-rate this time and locked one in at a decent enough 7.5%. My monthly payment is only a little more than half of what it had been before and it'll still be paid off years sooner than the original loan.

Refinancing doesn't magically fix everything, but goddamn does it give you some room to breathe for the first time in years.