You should probably go to the doctor.
I partially tore mine landing a jump in a mogul field (dumb). It sounds similar to your problem: I couldn't lift my arm for days and had to do these exercises where you walk your fingers up the wall with your arm straight. I can't remember how long it took to get better. Maybe a week to move decent again. Throwing a ball may be an issue for a while though if you do any of that.
You can tell it's your rotator by if it feels like the pain is inside your shoulder. Usually I can push on my arm just below my shoulder blade and feel it.