I dealt with this with my daughter. We discovered it in the hospital thankfully, her allergy was pretty bad.
I had to cut EVERYTHING out, mac & cheese, chocolate, milk, yogurt, sour cream, butter, cheese, cream cheese, cakes, doughnuts, ice cream, frosting, bread, I mean nearly everything is made with milk. I had no idea how much food had milk or some sort of dairy in it until I needed to cut it out of my diet.
I think a milk free diet can be done. It was harder for me because I don't eat meat. I am not a vegetarian- just don't care for meat often. For me it was milk free/soy free. because she was allergic to soy also.
She was still having a body rash and the green foamy poop at 3 months. Nothing I was doing was working so I had to make the difficult decision to stop nursing her. I still regret it to this day and wish I would have stuck it out more.
I ended up putting her on Nutramigen Formula. Ick.
It's a hypoallergenic formula, since she was allergic to obviously regular and soy based formulas.
She is going to be 2 in a few weeks and thank goodness is finally outgrowing her allergy and is tolerating milk products pretty well now.