Sorry to hear about your shoulder -- that really sucks. But take it from a guy who's been through two rotator cuff repairs (the doc accidently left in a couple of small tools during the first one, tearing a new hole in the tendon, so I had to go in for a revision surgery 9 months later). DO NOT PUSH IT. Follow your physical therapist's orders religiously and don't try to go faster than she instructs. Your object is full , not fast, recovery. The speed of your recovery depends on the injury you sufered, the kind of repair performed, your age and several other factors over which you have no control. The success of your recovery, however, is entirely up to you. Do precisely the amount and intensity of therapy excuses prescribed and no less -- and most importantly, no more -- and your shoulder will feel normal in about 6-9 months and be 100% in a year.
I'm the kind of guy who, if told to exercise with 5 pounds for 5 reps, thinks that 10 pounds for 10 reps would be twice as good (or at least heal me quicker). I had to learn to stop thinking that way. If you push your range of motion or weight or intensity or repetitions of an exercise too early, it's really simple to pull the repaired tendon right out of the anchors. Think of pulling a bow sting with several broken strands. It might hold ... But then again ...
If you're getting cut in June, your chances of pulling any bow by autumn, particularly a heavy enough bow to hunt with, are pretty slim. The good news is that if your injury is in your drawing hand's shoulder, the act of pulling a bow builds the small muscles in the back that stabilize your rotator cuff to protect against new injury in the future.
After my second surgery, I had complete recovery of a long, full-thickness tear and a couple of more bad tears in my labrum. I recovered full range of motion and all the strength I've ever had, with no pain or arthritis or anything else, within a year. I'm almost 60 and shoot a 62# Black Widow at least 100 arrows a day. But it took some time. I was lucky, though. I had a really hot therapist, a freezer full of ice and a few cases of Heinekins.
Good luck.