Most likely tennis elbow / lateral epicondylitis which is basically tendon inflammation. A brace/splint, NSAIDS(aleve/naproxen or ibuprofen - if you dont already have GI issues for no more than a few weeks), ice(20 min a couple times day) and rest on that arm(caused by excessive wrist extension and forearm pronation) is the most common treatment. If it doesnt resolve in a few weeks after that, go see your primary doctor.