Katie - I pitched baseball in college and tore my labrum but didn't get it operated on for 25 years. Unfortunately, they had to do mine twice as there was a 2nd tear.
My advice - get a good surgeon as mentioned above, do the PT and exercises exactly as recommended and take your time...patience really is a virtue.
I had one done in June and "tried" to bowhunt that fall. No chance, I carried it but never even pulled back.
I also bought a light weight bow and used that to build up to my normal hunting weight bows (52-65#), which I was able to handle the following season with no problem.
I personally slept in a recliner for about 6 weeks and take your medicines after the operation, don't chase the pain.
Best of luck.