Contrast baths work quite well for tendonitis. Soak it in cold water for a few minutes, then hot, then cold, etc etc etc. If the pain persists take an anti-inflammatory.
Either way rest it for a few days and take some time to figure out why this happened.
- Are you warming up with a general mobility warmup at the start of your workout?
- Are you warming up to your working weight on your exercises?
- Are you doing too much exercise that places repeated strain or impact on the elbows? A lot of isolation exercises do this, as does too much pressing, or impact forces.
Might also want to look into supplementing with glucosamine/chondroitin and fish oils if all of the above is okay and it still re-occurs.