Hi Jaime,
I have a 3 month old son that had a smiliar problem. In the last 2 weeks, I have changed to breast feeding on one side only for a 2 hour period. I think I had "over active let down" (over producing milk). By feeding on both sides at each feeding, your daughter might be getting too much foremilk and not enough hindmilk. The foremilk is very acidic. Without the right amount of hindmilk to balance the foremilk it could upset your daughter's stomach. I read a little about this online. I think it said that each breast has like 2 ounces of foremilk and 3-4 ounces of hindmilk. So if she eats full on oneside and then goes to the other side she might just be eating enough on the secound side to only be getting the foremilk.
By letting my son just eat on one side for the 2 hour period, it allows him to fully get the foremilk. I also started sitting him up to breast feed. I know it sounds stranged but online they mentioned that if the baby's head is above the nipple it keeps an overactive milk production from spraying to the back of the baby's throat. The baby can then use his or her mouth to stop the flow of the milk thru the nipple when the flow becomes too much. I think this has helped us as well.
I know the frustration you feel when you can tell your baby is hungry and hurting. When breastfeeding normally provides comfort for her,it is frustrating to see her in pain from breastfeeding. He has always been a good hungry eater but now he is so does not cry out while breastfeeding. We are both so much happier. Good luck!
A sympathetic first time mom,
H.