I have been dealing with elbow pain for 2 years now. Went to 2 different orthopedics and they both said the same, tennis elbow!!. I wanted to continue to lift hard so I have my physician give me a cortisone shot and it helped out great. If you dont mind shots go with it.
Cortisone shots just mask the pain. Its not a maintenance protocol and in fact you might end up hurting yourself more because the natural 'pain responses' of the body are masked by the cortisone shot. If its just plain miserable, then a shot will help it while it heals, but that doesn't mean you should go out and start doign the same stuff that irritates it in the first place. Take that time off to let it heal.
With regard to dealing with it - ICE is a huge help. Ibuprofen if its really bad, but try to not make it a regular protocol as it can irritate the lining of your stomach.
Personally I got my first exposure to what was described as the "opposite of tennis elbow" back in 1992. Over the years it has flared up, or gone away thru rest, ice, etc. More recently it has really become an issue. It seems like once you get it, it may recede and flare up, but never really goes away. You can work w/ different angles on your lifts, different grips, different bars (e.g. I strictly use an EZbar because the straight bar just plain old hurts).
Those little straps someone above mentioned did work well for me. I also used to use neoprene elbow sleeves, and more recently nylon sleeves. I don't like having a wad of neoprene pressing on my elbow joint on curl contractions and I found even the nylon sleevs would compress my arm to the point of discomfort, so I went to the pressure straps.
One thing that scares me about getting various flavors of tendonitis is that we tend to pretect the pain point by having other muscles try to do the work of the painful muscle or tendon. This then leads to other stress issues - basically surrounding muscles can start to ball up and cause other pain further down the road. I've found a good massage therapist can help break up some of the tensed muscle as well.