Your problem could have been described by myself.
I have the same pain on the right side which stopped me from benching for weeks, because the bottom stretch of the bench is just painful and pulls my shoulder forward. Furthermore, I also feel pain when i just pull my shoulder back like you.
I tried those shoulder extension stretches and it is exactly the spot which hurts. Whereas my left shoulder feels quite good i have a good stretch on the right side. I think this is the prize for months of bad bench form with shoulders going forward and neglecting the posterior shoulder and horizontal pull exercises.
This is my wake up call for good mobility.

Did you manage to solve your problem?