Lookout for milk hidden in certain products, like candy bars, and processed foods. You can check out the food allergy network
for products that are milk free. I wonder if the diarrhea your baby is having is normal. Infants, especially breastfed infants, have very frequent bowel movements. I couldn't change diapers fast enough. If there is no blood present, then I wouldn't worry too much. If you are still concerned, you could have your pediatrition run an analysis on a stool sample.