Lateral epicondylitis. AKA tennis elbow.
Grab the fingers of affected hand, and pull them back along the arm toward the elbow until it is just about uncomfortable. Hold for 15 seconds. Do this every time you think about, or the elbow hurts.
Repetitious lifting with the palm down, or hitting a backhand, strengthens the muscles on the outside of the arm, causing them to shorten, and puts pressure on the tendon.