Rotator cuff muscles are prone to tearing, and that tendency increases with age. A rotator cuff tear can be repaired, either surgically or naturally if the condition isn’t too severe. While nobody wants to force an arm or shoulder to move if it's frozen in place and painful to move, inactivity is a bad idea once the initial pain goes away and you can move the joint again. Inactivity leads to atrophy, which means that the muscles are wasting away, and then you have two problems to deal with rather than one. They should have given you a series of exercises to do when you hurt it the first time, and if not you should get some that are specific for the rotator cuffs. I have about 12 of them that I’m supposed to do every day, and actually get around to doing every other day or so. If I have pain, they actually make the pain better, and it stays better if I do the exercises regularly. The rotator cuff exercises are easy to do, but boring, because they take about 45 minutes to an hour that I would rather be doing something else. It's kind of fun to exercise if you can feel your muscles working, but if you try to make the rotator cuff exercises harder to get a better workout, then you're doing them wrong. It's just a matter of going through the movements to work these tiny little muscles that you can't even really feel (unless you tear one, of course). I'm supposed to do them for the rest of my life, or at least as long as I want to keep shooting the bow.
Also find Arne Moe's YouTube video on the rotational draw, which is easier on the rotator cuff muscles than a straight back pull.