I slammed on the side of my arm and has some pain at my rotator cuff area. I can move my entire arm around but it gets painful when I sneeze or cough.

Time. This should get better with time. Probably just a muscles contusion, or bruising. If persists for weeks to months, and inhibits daily activity, see your primary doctor for a proper evaluation. In the mean time, limit activity that makes it worse. Use ice intermittently, and consider naprosyn (naproxen) or ibuprofen if they are OK for you - ask pharmacist. Hope this helps!