IDK what the hell prolific shooting is, but I'm assuming it's a program where all you're doing really is SHOOTING BASKETS???
OVERTRAINING? You can do shooting drills EVERY SINGLE DAY. You can mix in shooting drills with upper or lower body lifting... Schedule you're strength program, and do your prolific shooting program with it, they won't work against each other.... If you do like upper body lifting RIGHT before you do your shooting stuff, it'll affect your shots for a little bit. The first day, maybe it'll take like 20-30 min of shooting warm up to loosen your arms again, but after like a few days, you'll get used to it and be able to shoot normally within 5-10 minutes of a shooting warm up after doing upper body work.