I've had three rotator cuff surgeries right shoulder, and yes I am/was right handed. I do everything possible with my left hand, I'm now a year after the last one and it still isn't right. Still on too many pain killers, maintenance at this point. I was a smoker and my surgeon said "quit" or he wouldn't do the surgery. I did quit and I'm grateful for that (used Chantex) and have no urge to start that again.
Be very careful on the Physical Therapy, my rotator cuff was torn loose after the 2nd surgery in therapy and the therapist did NOT recognize that I was in trouble. The doctor straightened him out, but how many others did he mess up?
This is very serious stuff - make sure you know what they are doing and what the results are supposed to be. Good luck!