Yeah the exercise isn’t something you do until the pain subsides. Then you need to work the muslces that support your ligaments (foreams, biceps, triceps), and hope that it doesn’t happen again 🙂
I came across this site, which could probably help you see what injury you have. It sounds like you may even have Bursitis? Which is mentioned at the link.
http://www.golfers-elbow.com/golferselbow.htm
And no matter what is actually wrong with your elbow, an elbow strap is a must. Below is a link of a picture so you can see what I am talking about. It helped me quite a bit. Then once my initial pain was gone, I just went to a neoprene elbow brace.