This condition is not painful, and it will usually resolve on its own within about a week. Nursing can continue. Blood in your milk will not hurt your baby. Rusty-pipe syndrome should not, on its own, affect your ability to feed your baby. Possibly you experienced severe engorgement following your baby's birth, leading to this syndrome.
Unresolved engorgement can lead to a diminished milk supply.
It is very important to nurse early and often as breastfeeding is becoming established in the first six weeks. Avoid the use of pacifiers and bottles, in the hospital, and at home. If your baby is having difficulty breastfeeding in the early days, allow him lots of practice time. Don't be surprised if he starts out just licking and nuzzling at your nipple. This is very normal.