I've never had MS pain, but I have had the type of shoulder pain you describe. Excruciating and long lasting. I had it my senior year in college. I played field hockey and spent the entire first semester downing advil and icing. It took several months to go away. Got some cortisone shots in the capsule but they only worked temporarily and apparently aren't recommended for younger people (I found out later).

Rest, ice, and advil were what helped. I did find out that I was triggering it/making it worse?? by sleeping with my head on my arm. I think that may be how it started and then I just aggravated it constantly by continuing to sleep that way and playing sports. Probably want to see a doc and get some PT. I bet some heat and ultrasound could help from them.

Good thing is that was 15 years ago and it never came back. See a doc so you can try to nip this in the bud.