David,
I suspect the blood is due to the damaged nipples, which could be caused
by either baby's suck or the pump.  Breastfeeding or pumping should not
be painful or cause injury.  I would examine both the pump and the baby
feeding to determine what is responsible for the nipple injury, so it
can be corrected.
--
Catherine Watson Genna, IBCLC  NYC  mailto:[log in to unmask]