Obviously, don't take medical advice on HN too seriously, but my uncle had shoulder surgery and was happy with the results. I have heard many more complaints about back surgeries making things worse than shoulders.
However, if available I would try to find a good Pilates/dance/sports instructor that has a Gyrotonic machine, which is built for repairing and strengthening shoulder muscles. I had debilitating back issues from sitting in a chair all day and a good instructor fixed it over a year through low impact Pilates. YMMV and group classes tend to be ineffective because so much of it is doing the exercises precisely correct - they were built for injury recovery
However, if available I would try to find a good Pilates/dance/sports instructor that has a Gyrotonic machine, which is built for repairing and strengthening shoulder muscles. I had debilitating back issues from sitting in a chair all day and a good instructor fixed it over a year through low impact Pilates. YMMV and group classes tend to be ineffective because so much of it is doing the exercises precisely correct - they were built for injury recovery