I used to play junior tennis and I had a severe case of tennis elbow once. You can do the hot/cold/ibuprofen thing, but ultimately the only total cure is to rest it for an extended period of time.
AFTER it gets better, I would recommend strengthing your forearm muscles via exercise (forearm curls/reverse curls/hammer curls) to prevent it from happening again. Most importantly, try to change whatever caused it in the first place. I know this sounds obvious, but if you're using your arm for a motion it is not ready to handle, you'll pay. I got it from actually playing tennis, and my forehand was way to wristy (usually not good), so I completely overhauled my stroke and had no more problems.
Yeah, heat all night long (heating pad) helped a lot. It increases blood flow to the damaged ligaments.
Get well soon!