I and others have switched from split to three under without experiencing any finger pain, so I don't think there is anything inherently related to three under that would cause the problem. You're probably dragging your fingertips somehow when you release the arrow. Make sure you're not trying to open your fingers. Instead, you should be relaxing your fingers and letting the string push them out of the way. Using a deep hook, in the finger joints rather than on the pads, may help you relax your hand. I know, both of these suggestions seem like they would make the situation worse rather than better, but they seem to work in most cases.
Until your fingers heal, you might want to try using a heavier tab, like the Martin Archery Mitt, sold by 3 Rivers. Then after a few weeks you could go back to something lighter, if you want.