You should consider the possibility of a bone spur. Doc will xray your shoulder but only an MRI can really tell you what its like. I had the same type pain you did. It turned out that I had a bone spur that rubbed a hole in the rotator cuff. Takes about 100 days to full recovery after surgery.
Told the Doc to check the other shoulder even though there was no pain at all. There was a spur and it had just started to rub on the rotator cuff but with no damage yet. Still had the Doc grind it off. It would eventually damage the rot cuff.
Had the same injury only right side though. After getting checked out I was told stop any overhead lifts for a least 6 weeks and go to physio or lose the shoulder. I was skeptical and pretty pissed about not being able to train properly but 6 months on im stronger than ever.
Also reverse flys. Apparently my anterior delt was more developed than my posterior delt from benching etc and neglecting isolating the rear delt area often enough.
I had something very similar recently (the arm under pillow hurting thing too lol). If your case is like mine: will slowly get worse and worse and more and more exercises start to cause the pain. For me it was OHP, then incline press, then bench press, then pullups, then rows. In short, it got to the point where I couldn’t do any upper body work.
Just going to the physical therapist and doing what she said was enough to help me. But I did have to take 3-4 weeks off of upper body work. It’s unfortunate but think about this seriously. Is squeezing in another 1-2 weeks of painful half assed shoulder work going to cause significant results that are worth fucking up your shoulder and having to take even more time off in the long run?
My PT had me doing external rotations, pushup-plus and scap retraction exercises. And pec stretches. (2x every day) Over time this helped and it is mostly healed now. Basically, I had weak stabilizer/postural muscles and poor scap retraction. Of course you will have to see what your PT says but in the meantime it couldn’t hurt to try doing some of these (only if they don’t aggravate it).