I started right to work on the same exact injury less than a week into my start at competitive swimming. (Too many pushups were tightening my chest too much for my back to keep me leveled out, and swimming pinched at my by-then-rolled-too-far-forward shoulder.)
My coach told me to stretch my shoulder every day, slowly and steadily (well, duh: it's a stretch!
![Wink ;) ;)](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
), for a few minutes. It felt better almost immediately.
While I didn't tear my cuff or anything that severe, I still say that if a month afterwards you can use the arm again, sit down on your floor with your legs out in front of you, and crawl your hands back until your chest/shoulder are stretching (or, of course, until it hurts so bad you can't breathe). Hold that for a bit, then do it again.
Then, stand up and find a wall. Put your hand on the wall a little more than shoulder height (arm fully extended), then turn your body away from the wall, stretching your chest and shoulder again.
Again, slow and steady wins the race, and if you start to experience more pain, go see a doctor ASAP.