My first treatment would be to tape the shoulder to support it. It is unlikely you have damaged every part of the shoulder, but that is has gone into a protective spasm. The tape would help to relax the uninjured areas and point me in a better direction.

With a fall, the first instinct would be an acromioclavicular (AC) joint injury. CAn you put your hand on your opposite shoulder? Any pain?

I would certainly suggest seeing a physio to get a proper diagnosis. Shoulders are complicated joints to diagnose when you see the person, never mind when you can't