I would try changing the way you are holding your gun so the weight is adjusted to somewhere else and not directly onto your arms. I shoot the CAR method since I'm a lefty but changed to learn to shoot right handed and left eye dominant. Doing that, my arms are pulled in and elbows aren't locked and my shoulders are bearing more weight than my arms.
I had a level 2 anterior cervical discectomy and fusion in mid November (getting old is tough! lol).
I get sore when I shoot but only the day after. My surgeon says it's fine and a good way to build my muscles back up.
Try some Aleve for a day or so and see if that helps alleviate any inflammation. Just be careful with the NSAIDs and your kidneys.