i really can relate to your situation i think. i took a really bad fall while running (tripped over a stump of a metal street sign--the stump was never removed from the sidewalk). i had never had shoulder pain before or much of any other pain. i figured at the time i just fell and whatever i did was a bone bruise or sprain and it would heal. i waited months before seeing a doctor. i had an mri which showed possibly a small rotator cuff tear. the recommended course was physical therapy which thanks to a new therapist got rid of all the pain. i thought i was home free but a year later i felt the original pain again. back to pt but this time i really wanted an mri done before doing anything. i had torn the rotator cuff. ok--got that fixed. i am a swimmer and several years later was diagnosed with a labral tear in the other shoulder. i tried to ignore this too prior to the diagnosis. i recently had that operated on.
i am writing with a word of encouragement. the rotator cuff surgery was much, much worse than the labral tear to recover from although i am not done yet. there is a huge difference. you will be ok. just find a empathetic doctor who is good and answers all your questions. then find a good physical therapist who is encouraging. (some are downers.)
i have been out of surgery 12 weeks now and basically doing ok. i have a lot of strength to get back. the doctor told me to begin a careful swim at 5 months. that sounds like a long time but it is not the end of the world. i have been exercising lower body and cardio since 6 weeks out.
this may make you feel better. i am not the best swimmer and probably a lot older. you will heal as well if not quicker than me i expect. you will get your range of motion back. you may not win the olympics but you will get back to swimming and i expect after you get over the initial fears ( which i am going to have too) will do great.
similarities to you---- 2 damaged shoulders but we will both recover.