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I had impingement some years ago. It doesn't sound as severe as yours. It took a couple of months of weekly physio sessions to cure it.
I've experienced shoulder pain a lot over the years and had surgery to both my shoulder and neck. In my experience, shoulder pain caused by a neck problem manifests itself differently from a problem in the shoulder itself, although there are some common symptoms as well. With the former, weakness in the arm (as well as pain) is common. C6/C7 neck vertebrae issues tend to lead to triceps weakness and higher up (C5/C6) can affect the biceps. There is a weird situation that can cause a crossover of symptoms where C6/C7 does affect the biceps and C5/C6 affects the triceps, but it's not so common. My C6/C7 disc was royally screwed and I had a few years of really intense pain in my neck, across the scapular on the left side of my shoulder/back and also down my left arm. I had the disc removed in 2019, a spacer and supporting rods installed, and my pain has gone from 10/10 to 2/10. Prior to the surgery, I'd gone from easily being able to to 30 press-ups to not being able to do 1. My *right* triceps muscle was simply getting no nerve signal and refused to work. Rather scary at the time, but i reckon I've got about 80% of the strength back. The weakness was on my right side, but the pain was on the left. Bloody awful pain to be honest.Now, the shoulder pain caused by a shoulder problem. I used to play tennis quite seriously and after many years of playing my acromioclavicular joint (ACJ) was knackered. I had physio and several steroid injections which did little to alleviate the pain and I ended up having the joint excised and the bones fused. Not pleasant, but it actually sounds worse than it was. I still play badminton from time to time and lift weights (sensibly) to maintain shoulder strength and stability. I have had other shoulder issues that were easier to fix. Rotator cuff and bursa sac problems can be resolved with physio, injections, exercise and rest, as long as they're not really severe. Self diagnosis is possible, but a good physio is the way to go. If you want to try some self diagnosis tests, these guys have done a few videos on shoulder issues - They're a bit comedic at times, but worth watching.Due to my ongoing neck/back/shoulder issues (I've had a fair amount of surgery) I'm always on the lookout for new treatments and exercises. I have to say, this book has been something of a revelation:https://www.amazon.co.uk/gp/product/1589096428/ref=ppx_yo_dt_b_search_asin_title?ie=UTF8&psc=1A lot of physios are now following its guidance. It simply involves hanging (as apes, our closest ancestors, do) in order to maintain the correct shape and structure of our shoulders. I installed a chin-up bar in my garage and use it most days, simply to hang from. It's not completely cured the problems I have, but it's definitely improved them, a lot. No drugs, no surgery, just hanging. Worth a try. Hope this is useful.