I had a similar problem following a bike accident. We flipped over with a Tandem bike. Bike and wife were fine because they landed on my shoulder.
I went to a Specialist for shoulders. He ordered x-rays and MRI. Nothing was broken but I could not lift a glass of water or turn the knob of my car radio. This is serious stuff. Biking was also a problem. It hurt.
I went to another specialist. He believed in therapy. I was ordered to use rubber bands and use specific motions. Oh, I forgot, there also was a cortisone shot and I was on Anti Inflammatory pills for a year.
This was 4 or five years ago. I no longer take pills. But I do the same exercise every day. My arm is about 90% of before the crash. I still avoid sudden jerky motions such as golf or tennis.
I know, it is no fun but such is life. I do not like operations and this doctor did not recommend it either.