Is the pain on the medial (on the side of your little finger) or lateral (thumb side) of your elbow? Lateral epicondylitis is the classic tennis elbow and is quite easily treated with the aforementioned remedies - rest, ice, ibuprofen 2-3 times a day (up to 800mg a time.) A steroid shot might be necessary for pain that just does not go away and is usually curative.
The medial epicondylitis (golfers elbow, as previously said) is much harder to treat, and that is something that I have been fighting with for some time - got it from squeezing tennis balls (!) until they popped (talk about repetitive movements, I used to do this all day sometimes...was almost a nervous habit!) For that, the treatment is quite different; slow, negative repetitions often promote tendon repair, as their blood flow is minimal (tendons are rather hypovascular) so healing is slow. In a similar fashion, wearing a cutaneous nitroglycerin patch has been quite helpful to me (dilates the subcutaneous and surrounding blood vessels, increasing blood flow to the area to also provide healing). Rest and ibuprofen actually didn't help that much at all - in fact, the rest made things just stiffen up and get weaker, which made things worse.
I would suggest going to an orthopedist, or sports medicine specialist if you can find one in your area. I consider myself lucky to have found my guy, who is quite advanced/progressive. (Most regular docs and even orthopods will just recommend the basics...rest, ice, etc. and as I said, might not always be the best way to go.) Good luck