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It takes a week or two to clear out. If it is a true milk allergy, there will be hidden blood in the poop that they can test for at the doctors office.
Avoid casein and whey, in addition to milk. They are in the ingredient list of almost all packaged foods.
You still need calcium to BF, so take a suppliment and drink rice milk with cacium added or OJ with calcium. Many babies with milk allergy are also allergic to soy.
My baby was so allergic to milk protein that she got sick when I ate MIL's food made with butter. I had to avoid everything for the entire 6 months I BFed. I was tired of it and eventually switched to special formula.