Tore mine maybe 8/9 years ago snowboarding, trying to master 360s - came round short and at a funny angle and hit the deck hard, catching my elbow in the snow which pulled my arm from the shoulder socket. Saw a physio and got the exercises and the big rubber band but didn't stick with it properly and soon aggravated it.
For the next couple of years it didn't get the chance to heal and the shoulder dislocated maybe 20-30 times - riding, playing football, sneezing - got to the stage where I could put it back in without much bother, but I couldn't carry anything in my right hand or throw anything. I'd been on an NHS waiting list for a corrective operation since the start, but heard nothing at all.
Someone I spoke to recommended swimming breast stroke as a way of strengthening the muscle, so I did - swam about a km and a half at least 4 days a week for a year or so, which was sore at first but became easier after a while and I could feel the benefit (and enjoyed the fitness payoff).
Since then I've dislocated it once, maybe 3 years ago, smacking into a rock face snowboarding (which I had to reset myself by grabbing a binding strap and trying to stand up) - just carried on swimming and everything was fine.
No dislocations since (despite a few incidents where I felt certain it would happen) and no pain throwing and normal strength. There's a chip out of the top of the bone in my upper arm (can't remember what the bone's called) which can cause a sharp twinge when my arm's twisted a certain way, but that's rare.
Everyone's injury is different of course, but I'd certainly recommend swimming breast-stroke - its more or less the same resistance movement as the big rubber band exercise. Takes a while to have an effect, but worked wonders for me.
Good luck!