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Oh man I feel you. I have occasional shoulder and hip pain and I sleep on my side. I’ve seen special pillows for shoulder pain, is that something you’ve tried by chance? Thinking about this kind: https://www.amazon.com/dp/B07GTB5BFB/
If you’re able to invest money into a product then definitely this pillow. It raises you up a bit and allows you to slip your arm through the hole so that your shoulder is not compressed when you lay on your side. There’s another version with a higher wedge that does the same but also can help reflux with the higher angle if that’s an issue for you as well - 2 birds with one stone. It isn’t cheap but if you’re only comfortable on your side I would consider it well worth the investment.
If you don’t have that much money to invest in a product this isn’t as good in comparison but might be a decent compromise: