You didn’t say waht your exact injury was. Rotator cuff tendonitis is caused by overdoing it and/or not warming up properly. I don’t dispute the mechanical argument either but young players usually aren’t taught how to warm up and almost never taught how to strengthen their rotator cuff.
Now, onto the topic of weights and pitchers…
I see nothing wrong with some weightlifting. However, bench pressing and any kind of pressing movements where you raise your arms over your head are not recommended for pitchers.
This is where my knowledge ends, I can’t give you the ideal weight lifting program for pitchers. I can tell you that I got fairly strong in the squat (405 lbs for reps) and also in the bench press (300 lbs). The hardest I ever threw was 82. I was 5’11" and 198 lbs at the time.
I would advise you begin a program to get and keep your cuff strong as well as a program which develops the strength you need to improve as a pitcher. Begin each throwing session by warming up properly which should include rotator cuff exercises.