I don't think babies can be allergic to breast milk, I thought its only if mother drinks cows milk or eats dairy products that baby can be allergic to. I think I read that in an article.
Hi i had a huge milk allergy as a baby and had no problems with my kids being allergic at all. (bf 3 kids) good luck :)
By milk do you mean breast milk or dairy based formula? I'm going to assume however that either allergy could be passed to your baby but I have no idea what the likelyhood is. In the event that your baby has a dairy allergy you can breast feed but you would need to remove dairy from your diet. I don't know what the options would be if your baby is allergic to breast milk.