Bleeding is not normal - you need to see a lactation consultant ASAP! If the hospital where you delivered has one, that is where I would go first. And I mean like this morning - they are often closed on weekends. If that doesn't help or if you don't have a lactation department, then call a lactation consultant. They are often covered under health insurance but if not - sometimes they will see you for a sliding fee or even free the first time.
BLEEDING IS NOT NORMAL. I would guess you have one of a couple of things going on - your baby is not latched properly. Most pediatricians are NOT trained lactation counselors!!! OR - the shape of your baby's mouth is not compatible with the hold you are using. My son's mouth has a very high and narrow pallate. That made it hard for him to get a good latch in certain positions. I worked with a LC for about a week and we then nursed over a year! And yes, I was bleeding, and yes, it hurt something terrible.
The other possibility is that you have inverted nipples and your baby is having a hard time drawing them out. Again - a lactation consultant could look at you and advise options.
None of these things would mean that you can't nurse - you just need some professional help!
http://www.floridahospitalwomen.com/en/the-baby-place/bre...
http://orlandohealth.com/winniepalmerhospital/BirthingSer...
http://www.patlc.com/lactationvisits.htm
http://www.breastfeeding.com/directory/states/florida.html
Do not delay - get help today so that your breasts can heal, and you have a great breastfeeding experience. It is true that nursing might be a bit uncomfortable at first but never absolutely painful and not bleeding.
I wish you all the best. C.