Milk allergies are considered the most common food allergy in children. This generally involves cow’s milk, but milk from buffalo, goats and sheep also can cause a reaction. Milk allergy symptoms include wheezing, vomiting, hives and digestive problems, according to the Mayo Clinic. Luckily, milk rarely involves a life-threatening anaphylaxis reaction, which is a whole-body reaction that can cause airways to dangerously tighten. Children tend to outgrow these allergies after age 3.