My perspective, if it helps...
I have a similar thing going on and started physical therapy a few weeks ago. on 11/24. Like you, I didn't have a specific injury or any event or surgery to recover from. Just pain and discomfort in certain positions and with certain movements, and intermittent pain in the shoulder area, especially at night.
As much as I'd like to choose a specialist in strength training, insurance doesn't work that way. I go where my referral sends me. Fortunately they're pretty good, as I went to this practice last year for a similar situation with my hip, and they helped me solve it.
So far, it's going well with the shoulder rehab. They diagnosed weak rotator cuff muscles. As I understand it, when certain muscles are weak and not doing what they're supposed to, and I am doing hard things with other muscles in the area (i.e. I'm doing a lot of things with a heavy barbell), the small weak muscles get overworked, tight, and inflamed. Inflammation in the muscles in the shoulder area leads to things getting even more cramped because there's not a lot of room in the shoulder joint. This leads to a sort of secondary impingement when I move my arm up overhead. This leads to more inflammation. Etc.
So the solution is to do a series of 4 stretches (because weak inflamed muscles get tight and cranky, and restoring full ROM is helpful to properly working the muscles), about 10 seconds of 10 reps in each stretch, one for each of the 4 rotator cuff muscles, then do a rotator cuff strengthening series using bands and about 4 sets of 10 reps of 4 different exercises. They do a bit of manual stretching and manipulation to loosen up the shoulder, too. This clinic also does dry needling, TENS, and other things... but they don't feel that it's needed for this issue right now (I agree).
I was pretty sure before I went to PT that I needed this type of work, and had a lot of good suggestions from people when I expressed my problem with painful push-ups in
this thread. However, I was really hesitant to add stuff to what I was doing when my muscles felt overworked already. So it helps a lot to have a PT that tells you exactly what to do.
Not sure if this helps with your situation, but part of the lesson for me is that it's probably not a super complicated situation. A PT clinic that deals with common problems is probably going to help you just fine. Chances are good that if you get on the right track to improving things, your body will be able to heal.
Good luck and let us know how it goes...