The recommended dose for mild to moderate pain in adults is 200 to 400 mg orally every 4 to 6 hours as needed. Take with food or milk to prevent upset stomach.
The weak hand points to nerve involvement, most likely a separate issue from the deltoid pain.
I wonder if experimenting with different positions on the handle bar while riding might provide some relief for the hand issue which could possibly be due to either ulnar or radial nerve irritation (especially if you don't already change up your hand positions) If the wrist is bent when grasping the bars, see if there is a position where you can keep the wrist straight. A soft brace at the wrist (which are found in most any drug store) would help remind you to keep the wrist straight.
Definitely a physical evaluation is needed to determine the cause of what sounds to be two separate issues.
Please feel free to update with findings when you see the orthopedist.