If you are not in season, take at least a week or two weeks off from throwing. Usually tendonitis is due to overuse, or putting too much on your arm before it is properly conditioned.
Anytime you feel pain or an ache after a game, it is a good idea to ice immediately after coming out of the game, and to take an aspirin or Advil to help reduce the inflammation.
It sounds like you MIGHT be throwing with improper mechanics, or incorrectly throwing a slider or curveball, so you may want to have a reputable pitching coach take a look at your motion.
Rest is usually the best thing for tendonitis, followed by easy exercises and light throwing. Often it results from doing too much, too soon. A pitcher should ease into his highest pitch total on a gradual basis, over several weeks. Unfortunately, many HS players go straight from zero pitches to 80, 90, 100+ in less than two weeks (not a good plan).
Better to start with 20-30 pitches a day for a week, then build up to 40, then 55, etc., until you get to where you need to be.