See if anyone you know goes to a chiropractor. You may be able to get a free evaluation. I know several who will do your first visit & x-rays for free if you get a referral from one of their current patients. If they are honest they will tell you if they can't help you.
Also if you decide to keep going, they should be able to make financial arrangements. My insurance stopped paying for my chiropractor a while ago (even though I have scoliosis) so the doctor worked out a payment plan so I only pay $20 a visit!
To prevent this from happening a lot, you may want to do some stretches first thing in the morning, and maybe find an exercise program to strengthen your bath muscles. You can throw your back out picking up a paper clip, it just means there's been a problem for a while that finally caught up with you. Good luck & feel better!