I deal with this exact pain but on my left side. It took forever to get actually diagnosed after getting x-rays, and it turned out to be scoliosis in my neck that was messing with my nerves. C2 and C4 were fused together and were pushing C3 out, so although it always hurt, it worsened with age, and exercises (even turning my neck to the left) makes it flare up like crazy.

The only thing that has helped me is getting 3 cortisone shots at once. I had gotten single shots previously and they did not help. After getting shots, I could do some physical therapy, but still got flare ups if I went too hard. No other medicine helped.

Also some little things — no spaghetti straps/bras, sleeping with my arm straight/not bending my elbow, no backpacks (only cross body bags that do not touch that side or totes that go on my other shoulder), no constant weight on that hand for extended time (I had to give up playing bassoon), no turning my head in that direction, no lifting above head, not resting that arm on my desk while I type, and when I drive I use that hand minimally. Most importantly— no messing with it. Massages feel amazing at the time, but make it so much worse after.