Yup. An x-ray is pretty useless. I find it hard to believe any physician simply prescribed an x-ray.
An MRI is necessary, preferably a 3T.
After the MRI you can decide on a course of action.
The differential diagnosis involves choosing between progressive degenerative spinal disease, and a simple vertebral subluxation.
It sounds like a verterbral subluxation, which respond well to mild intermittant traction and range-of-motion exercises. The intermittant traction is five to ten minutes six to eight times a day, with range-of-motion exercises in-between. The important thing is to avoid a frozen shoulder by moving through the limits of pain. The problem is with such injuries a patient tends to "self-splint" and eventually can't move the arm and hand.
The chances are it did not come from pushing a gurney. It could have come from lifting a patient.
Treatment used to involve prednisone, but lately they have been prescribing a transdermal lidocaine patch, which is worn for up to twelve hours.