My son was generally colicy and had a lot tummy discomfort. We found a tiny bit of blood tinged mucous in his diaper, a sign of a milk protein intolerance (which he outgrew). I had to cut the milk and soy. My Pediatrician gave me a list of ingredients that come from milk & soy protiens. The list is extensive. And, you'll have to learn how to read the labels. I was told not to expect any changes for about 2-3 weeks.
My advice would be to have your daughter's diaper tested for a presence of blood. Then you'll know more before embarking on the elimination diet. Cutting dairy is do-able but, not as simple as you'd think because it is in bread, hot dogs, flavorings and things you would not expect. And, you just can't cheat - even with the tinyest piece of mac & cheese.
For us, things did greatly improve. But, I did end up weaning him at 4 months and put him on Nutramagin (sp?) by Enfamil. That was when he started sleeping through the night and we all got our sanity back.
Good luck!