Is the pain on the inner, outer or middle of the elbow?
Inner is golfer’s elbow – technical term is medial epicondylitis if you want to do a search.
I first noticed mine when doing skull-crushers. The pain started small and in only one elbow, but soon intensified and spread to both. Eventually, my elbows bothered me doing many other movements as well – particularly extension work.
I’m still dogged by my elbows today, but they’re MUCH better than they were a year ago.
To go with the good advice already offered here:
1.) Take a week or two off from training.
2.) Ice the affected area(s) twice a day.
3.) Oral OTC anti-inflammatories are good, but try to find a topical version like Ibunex.
4.) Neoprene sleeves are good, but as mentioned above, forearm bands are a little better at reducing the friction during exercise.
5.) When you start back, warm up thoroughly (especially the elbows) and avoid ALL movements that place DIRECT stress/pain on the elbows for a while. If and when you can do extension work, be smart and don’t go too heavy or deep in the bottom portion ROM.
Overhead extension work can be hard on elbows, but is important for fully developing that long head of the triceps. Larry Scott was a big proponent of kneeling cable triceps extensions, and when you’re ready you may consider giving them a shot
(see pics at bottom)
They allow for a good, deep stretch without stressing the elbows quite as much.
One final thing to remember is that tendon inflammation is often caused by repetition/overuse – not necessarily weight.
That’s why people can wipe out their elbows swinging a tennis racket. And how much does that weigh?
Even after you’re better, consider reducing the volume of extension work you do, particularly if you’re prone to developing tendinitis. And it sounds like you are.