Quite a few archers suffer from shoulder injuries. I assume this is a result of two things. First, pulling bows that are too heavy for the shooter's shoulder. "Too heavy" is relative, of course; some people can pull 90# bows with no injury, while others get shoulder injury from much lighter weight bows. The second thing is that pulling bows works only certain muscles in each shoulder, overworking some and underworking others, leading to an out-of-balance condition. If we would shoot both right and left-handed bows an equal amount of time, it might help, but few of us want to do that.
Before I got serious about archery, I was a rock climber and so was able to crank off a lot of pullups. When I started shooting bows, I was able to pull a 65# bow fairly easily, and I never really wanted to pull any heavier bow than that. Maybe since I never tried to work up to a heavier bow, I haven't had any shoulder injuries, but I think if I were going to do that, I would probably want a balanced exercise program that would work all my major and minor shoulder muscles. And I would want to be tuned in to my body, so if I started getting shoulder pains, I wouldn't do things that would aggravate them.