Hello dear and welcome to the medhelp forum. Since you fell on your back, you could have sustained trauma to the intervertebral disc that is the soft cushion interspersed as shock absorber between adjoining vertebrae. Any herniation, degenerative changes or traumatic damage to the soft tissues may be best picked up on an MRI scan of the spine. Consult a neurologist as soon as possible for evaluation to enable time appropriate intervention and prevent deterioration. Management would be according to diagnosis, painkillers, hot fomentation, epidural injection of steroids and physical therapy if disc pathology is diagnosed. Wishing you all the best.
A scan might be more helpful, you can get a CT scan that is less expensive and less bother than an MRI, I think your regular doc can order one for you. I've had X-rays before, and while they do show a lot, I was so surprised when years after I had tore up my foot somehow and X-ray said I was fine, I had a scan done of that same area as part of a body scan, and do you know they found fractures in my feet!!! No wonder it hurt so much!!! As for what they might do if your scan turns up something, it really boils down to giving you some better pain medicines and perhaps getting you in a back brace, and maybe getting you into physical therapy, I don't know. A specialist, which your doc can refer you to also, like a neurologist or orthopedist, depending on the problem, can decide on a treatment plan.