I spent a few years in college as a sports medicine major, and am in the human performance realm as of now. basically an overhand type shot is going to wreak havoc on a lot of people's shoulders sooner or later. ask a disc golfer who has been around the game a while and they will tell you, but aside from that, rotator cuffs can be a rough thing to rehab properly.
like posted before, doing rotator cuff circuits with bands.......internal and external rotations with the arm 90 degrees from the body and tucked against the body, as well as various lateral and anterior raises....all this will help somewhat. unfortunately, since overhead shots is a relatively "violent" movement, exercises done at a slow rate will only help so much.
basically the reason that your rotator cuff hurts so bad a few hours after throwing is because when throwing, the rotator cuff must slow down the arm to protect the joint. often the arm is moving at hundreds or thousands of degrees per second, and the force that the rotator cuff must produce must be applied very rapidly. this can produce extreme soreness, and even tearing forces (hence why many baseball players tear their rotator cuffs)
so in conclusion, do the band stuff, but once you become proficient at it (could take 4-8 months), you need to attempt to emulate the higher decleration speeds with the bands, or find a cable machine at the gym that will replicate the higher velocities. until you can do this variation of the exercise effectively, i would try to stay away from overhead shots unless they are absolutely necessary.
any q's just message me,