My son has a milk allergy, and we found out the same way. He never had a problem when nursing (and I wasn't dairy free), but when we started supplementing with formula, he began having problems. He also had an allergy to soy and peanuts. Apparently the protein in dairy is very similar to the soy protein, so a lot of people allergic to one (although not the majority) are allergic to both. There are a lot of resources for you to tap into, and an increasing awareness about allergies. Babies outgrow allergies. Not all the time, but the allergist we saw said that a fair number of kids allergic to dairy are no longer allergic by the age of 5.
Because my son was allergic to both dairy and soy, we had to give him Alimentum, which was expensive, but we often bought it cheaper through Craig's List. Depending on where you live, your insurance might help you pay for it or it might be reimbursable through a medical spending account.
If the allergy continues, you will need to be vigilant about what he eats. If he is in daycare, you will need to review everything that they give the kids -- not just the menu, but all of the ingredients for everything that is served. We ended up just bringing in our own food -- we couldn't count on someone realizing that a simple decision like cooking the broccoli in butter one day could have serious consequences, and we found that almost everything served at the daycare had soy in it. Also, your doctor can give you a list of ingredients to avoid, casteine (sp?) is dairy, for instance. We had to get an epipen, but fortunately, never had to use it. We carried it everywhere, had one at home, one at day care, and one at the grandparents' house. You should also keep Benedryl handy because your baby might be allergic to another food when it is intorduced.
My son is 18 months old, and he still tests positive for dairy, but he is no longer allergic to soy, which has opened up so many options for us. In addition, his levels have dropped for dairy, and he will get tested again in the summer. He is no longer testing positive for peanuts, but we are still avoiding all nuts and seafood until his is 3 and eggs until he is 2. Doctor's orders.
Before he was cleared for soy, we continued him on Alimentum and also gave him rice milk. Rice milk, however, doesn't have much protein, which is why we had to still give him the formula.
Hope this helps!