In reply to Stevie989:
Do you mean near the end of the fingernail, on the corners near your fingertips?
I get this pretty often on my pinkies. It's usually when the temps are low and I'm really crimping hard. Seems to be caused by the stiff/dry flesh being twisted/squashed away from the nail, causing a slight split. Regular moisturising can help, but the biggest difference for me was moving away from Metolius chalk with drying agent and getting some plainer stuff.
If it gets very sore I can sometimes 'trim' the corner of my finger (ie clip the dead/dying skin near the split) which seems to reduce the leverage on the cut and help it heal faster. This is obviously not ideal and can be painful in itself. I assume it also comes at high risk of infection, heavy bleeding, death etc etc.