When I injured my wrist in a fall (many years ago) my basic first aid training told me that it was far more likely to be a fracture than a sprain because
(a) it was 'direct impact' injury, with the bone striking the pavement, rather than a 'tear' injury, where soft tissue is strained ; and
(b) I could identify an exact point from which the pain was emanating, rather than the pain coming from a more general area.
However the hospital staff couldn't see a fracture on the X-ray and decided that it was just a sprain. A fortnight later though I returned to the hospital, still in as much pain as ever. The original X-ray was re-examined and a fracture was then seen.
So just because the hospital staff couldn't see a fracture on your X-ray, it doesn't mean that your shoulder isn't broken.