Speaking from experience (I had tennis elbow for over a year). Get yourself a tennis elbow band, that goes on your forearm. You can find them on amazon. I was a big fan of the Mueller HG80 forearm band. It was cheap, comfortable, good material and most importantly, really helped alleviate the pain experienced in my elbow. I was actually able to continue to do whatever lifts I wanted, while wearing the band, with next to no pain. I used it on and off for about a year. My tennis elbow pain subsided after the year of use. I haven't used them since and my elbows feel healthy.
"Our bands work by compressing the upper forearm and absorbing the forces which are transmitted through the soft tissues to the point of pain on the outside of the elbow. They also change the angle at which the tendon works at the elbow which changes the forces which are applied to the tendon attachment allowing the injured area time to recover"
In terms of exercise selection...just do whatever doesn't hurt your elbow. Try to do your exercises with overhand grip or neutral grip whenever possible.
The exercises that caused me the most pain before I got the band; Anything underhanded (Chin ups, underhand lat pull downs etc), direct bicep/tricep exercises (Bicep curls, skull crushers etc), bench press. Avoid fat gripz, thick bars and once again an underhanded grip.
Lastly, go see someone about it. Rehab would be the most beneficial, and they'll work with you on forearm soft tissue work.