My first suspicion when somebody like yourself has a grumpy shoulder is that you've got a mis-match with your racquet (and that's without even seeing your hit some balls). Maybe it's too heavy, maybe too light, maybe something else. Poly usually irritates a player's wrist or elbow, but if it's an especially low-powered setup, it might also trick a player into overcompensating by swinging too hard too often to put some zip on the ball. A few hours of that can put a lot of strain on a shoulder.
The easiest way to make a substantial change with your gear is to dump the poly for the short term. Easier meaning cheaper than shopping out a different racquet and adjusting to that. Try a couple rounds with full beds of syn. gut or multifiber and see how things progress with a significantly softer layout. Your shoulder health is a higher priority right now compared with any wow factor you get with the poly. A few weeks of hitting with a softer alternative should either make a difference or not. Poly isn't for everybody, so maybe it's time to sort that out for yourself.
If you can't live without some poly in your life, there may be some kinder-gentler options. Locals who use me for stringing have had great success with what I think of as a skinny poly hybrid; a light gauge poly main of 1.20mm or lighter with a syn. gut or multifiber cross. For a while now I've used super affordable Isospeed Baseline combined with a few different crosses including Gosen OGSM, Volkl Classic Syn. Gut, and Prince Premier Control - all in 16 ga. In a 98"-100" frame, it seems to run fine tensioned anywhere from maybe 48-55 lbs.
This skinny poly hybrid brings a degree of poly performance to the equipment equation (spin) without going as firm as a full bed of poly. It also seems to have the advantage of not turning dead too drastically with a multi or syn. gut in the crosses to keep some resilience there. Although I don't play with polys, I've sampled this layout and it's similar to the firmness of a bed of syn. gut - not what I'd consider to be uncomfortable. And it's never irritated the arms of any players in my circle who have tried it.
I also haven't tried the gut/poly layout described in post #4, but I'd bet that it can offer a lot of upside once the tensions are dialed in.