I'd say you should use dumbells then, or a z-curl bar (with a fairly pronounced curve on it). I had the same problems with curls. Dumbells allow for a more natural movement of your hands (as opposed to a straight bar which puts your hand in a completely unnatural position and put strains on your wrists as you try to handle weight - I'm not sure but I think that can cause tendonitis). With the z-curl bar, I also found that a narrow grip made it easier. When this happened to me, the pain would stay and I had to slow down on the curls. I don't know about the skull crushers, but when I do the french press, I also use a curl bar with a narrow grip. i've managed to still do good bicep workouts, but straight bars are definitely out. I have also done forearms exercices to try and remedy this problem, by strengthening my forearms, but I'm not pro and could not tell you whether that was a good thing or not, even though it seemed to help. Anyway, hope this helps and good luck!