When you do skull crushers are your elbows supposed to hurt afterwards?
They're not supposed to. However, even though I used perfect form, my right elbow would feel like it was burning. I have since abandoned them and have moved to doing tricep kick-backs.
That's the problem with tricep isolation exercises. They can be tough on the elbow joint. Some folks can tolerate them without any apparent trouble, but not everyone and you don't want to mess up your elbows. I've never had trouble with the lying tricep press (skullcrusher)but tricep pushdowns are murder on my elbows. I suggest you experiment with other tricep moves. Dips are great. If seated or standing overhead tricep presses also cause you discomfort, try using one solid dumbbell held with both hands and let your elbows point out to the sides instead of forward. Close grip bench presses are another good tricep movement. Protect your elbows. You'll need them for a long time.