I had the same problem after giving birth and no one was able to help, so I did some research on my own and discovered that it was my hormones that caused constipation. To solve the issue I had to omit meat, eggs and milk from my diet. Almost immediately the pain I was experiencing while having a bowel movement went away. Hope this helps.
Often we get our first hemorrhoid during childbirth, due to the straining to push the little bugger out. I would cut back on the fiber, too much of this will harden stool also and constipate you. A hemorrhoid would explain the pain and bleeding, but this needs to be addressed. I'm sure you're still sore from the birth of your baby on top of this too! After my daughter had her son, she had severe pain with what she thought was a hemorrhoid, and went to her GI doctor to have it removed. Turned out to be an infected stitch! Have you tried prune juice? Colace has never helped me or my daughter. Miralax is good for hard stools, it is over-the counter and not habit forming, and will definitely loosen the stool. This is what I would use, and if this problem continues, I would see a GI doctor.
Congratualtions on the birth of your baby!