Wait a minute...isn't tennis elbow something that only tennis players can get? I mean, that's why it's called "tennis elbow," right?
Well, yes; but tennis elbow, which is an inflammation (and sometimes a tear) of the tendon that runs up the side of the arm next to the elbow, can happen to anyone who swings their elbow a lot, especially with the violent motion required to lob a tennis ball over the net -- or the throwing motion used by a baseball pitcher. The exact cause of tennis elbow isn't known, but it seems to be another repetitive stress injury caused by constant strenuous use of the arm muscles, resulting in tiny tears, cell death and increased pain when the muscle is used.
A similar condition, also suffered by pitchers, is golfer's elbow, which is an inflammation of tendons on the inside of the elbow rather than on the outside. And, yes, golfers get it too. Both can be treated with anti-inflammatory drugs, ice and, of course, rest and time.