Might be onset of frozen shoulder syndrome. Often only cortizone shot may help. But this is guess work plus having had the syndrome on my part. For all I know, your pain could come from a vaccine shot. Even gall bladder problems or heart disease can cause chronic shoulder pain. A doctor might sort this out, given time.
Remember, I'm not a medical professional. Any suggestions here actually can potentially make things worse, given I have no way of knowing the underlying condition. Any suggestion I have might work but might waste your time when it would be better being used to sort things out with a medical professional. Just because the shot or pain reliever proved ineffective is not a reason to suppose the next form of treatment on the doctor's check list also will not work. But serious chronic pain is nothing to ignore as it will wear you down in short order.
Till then, there are specific stretches which might help if it is related to muscle injury or frozen shoulder. The sort of pain you are talking about tends to finally make it very difficult to sleep.
Upper Arm Pain Exercises Medi Dyne
You might also google for exercises on the Mayo Clinic site. That site has a symptom checker too and might help you rule out some things.