There have been reports from bartenders and others who repeatedly turn the hand palm up and palm down. This problem is not common but has been described by violin players, swimmers, military personnel, and bartenders.
The condition is thought to be a nerve palsy called posterior interosseous nerve (PIN) syndrome. A branch of the radial nerve in the forearm that supplies motor (movement) function to the extensor muscles of the thumb and fingers is affected.
The repetitive motion of the forearm causes muscle contraction of the supinator muscle. The nerve gets pinched by this muscle as it contracts and especially if it gets built up in bulk from constant use.
It would be a good idea to see an orthopedic surgeon or hand specialist for an examination and proper diagnosis. You may be able to benefit from a special splint to rest the muscle and nerve while still allowing you to do your job. Antiinflammatory medications can help reduce any swelling. Rarely, more invasive treatment such as surgery is needed when there is a tumor, cyst, or scar tissue pressing on the nerve causing the same symptoms.