Breast fed babies and allergies
Babies are rarely allergic to breast milk. Humans are made to drink breast milk only so being born allergic to milk is basically a death sentence (before formula, that is). Less then 1% of all infants in the world are born with true lactose intolerence. Children who are lactose intolerent usually become so after the toddler years when we're not really meant to be nursing anymore.
If your baby seems to react after nursing then there are many other things you can look into. They could have acid reflux or they could be allergic to something you ate (nuts, eggs, berries, non-human dairy, etc.). I would start by taking out any possible allergen foods from your diet and seeing if that helps. Then slowly add in each food one by one and look for a reaction until you figure out which one is the problem. If nothing helps try contacting your doctor to look into acid reflux.