(natural)
I used to ritualistically develop broken shoulders from benching. I always continued training, but I would discontinue all bar benching (stay on db) and do no direct shoulder pressing. Eventually, they would subside and I would continue. The free range of motion of DBs is much, much better. You can naturally adjust to discomfort.
Haven't had that problem in maybe 5 years, though, since I learnt to tuck elbows properly when benching. Used to destroy shoulders pretty much every 3 months of bar benching.
Regardless of what you do, you MUST get over your hangups of not training a body part and do something - you have had a lot of treatment - but you have trained through it, which is something I probably would have done, too - but it's wrong and in the future you'll admit that.
At the very least do not directly train shoulders.
By the way, I have pathetically weak shoulders from avoiding them (they aren't small) and even at this low weight (dieted down), I can be sure of bench pressing 165kg+. There are people in my gym who probably have better shoulder press and can't press half that. That's the reality of shoulders. They aren't that important in any big movement.
It's not as bad as you think. I probably have a military 1rep max at the moment of about 85kg (if I'm lucky).
I have had to not bench for a year and a half before. That's bad.