I had X-ray for my neck and nerve check on my hands and lower arm. They found some little things on my neck and nerve pinch on both hands and arm which needs surgery. Doctor said I need to do those exercises he gave me. He recommended that surgery will not resolve totally as I have neuropathy. He said I will have pain in my arms due to things on my neck. My pain on my right shoulder happened after a day later. So I have to have X-ray taken.
I am a strong fan of physio as an early port of call for such issues.
I have a congenital back issue which a surgeon said he could operate on ten years ago (I got to the stage where I couldn't stand for more than 30 minutes without pain), but physio strengthened my muscles so that the issue has completely resolved without surgery. (Disclaimer, the surgeon did say that physio might resolve things so that surgery would be unnecessary).
As for my two (luckily not at the same time) frozen shoulders I "toughed out" the first one and it took 3 years to heal, with physio in the final year. I had physio for the second one immediately and it healed much more quickly (less than a year?).
Obviously mielage may vary but there are a lot of things that physio can do for many issues, even if they can't solve them.
My recommendation is to do your exercises. Good luck.