I too had extreme pain when I first began to breastfeed. Everyone said "Breastfeeding does'nt or should'nt hurt." so I thought I was doing something wrong.
In truth it does take some women's nipples to adjust. As it did mine. I say for the first 2 weeks or so it was really hard. When my daughter first latched on I would have to count down back from 10 to get through the pain. I would clench my teeth and just breath.
Once I got over the initial latch, and her creating the suction, the pain would subside and she would feed. I would be slightly uncomfortable while she fed, but it was really that first minute of latching that was the toughest. I also had a blood blister on the second day after her birth that lasted 3 or 4 days, making the feeeding/latching extra tough.
With that said, if you are experiencing pain throughout the duration of the feeding you should make sure that your baby is latching correctly. If such is the case, as lilirose said, it may be time to call in the lactation consultant.
Don't give up - I really felt like throwing in the towel there on a couple of occasions. I am so glad I didnt. The bonding experience, the lovely look in baby's eyes, and the best mama milk for her made it worth all the pain in the tears in the beginning. Good luck and keep going!
**edited to add Have you tried using lasinoh on your nipples., maybe you are bleeding because your nipples are chapped. this helped me. also apply before you go in the shower - the hot/cold water can make the chapping worse!