Is it possible to cause an allergy to milk by giving my two-year-old too much?
No, allergies do not occur that way. Allergies occur when the body's immune system "reacts" to certain proteins in the food that we eat. The immune system sees the substance as "foreign" and makes specific antibodies to it or has cells that release irritating and inflammatory substances in response to the protein. Thus the amount of the substance causing the allergy generally doesn't matter. If a child is going to be allergic to a particular food, the symptoms will occur with just a small amount of that particular food. The problem you may be confusing allergy with is lactose intolerance. Lactose is the major carbohydrate or sugar in milk, and some people have difficulty digesting it. They have low levels of an enzyme called lactase, which is used to break down the lactose. Symptoms can include bloating, abdominal discomfort, constipation, or diarrhea. A child who has lactose intolerance will have greater symptoms when he drinks more milk or eats more milk products. He might have enough of the enzyme to manage a half a glass of milk each day, but not enough to handle three glasses and a bowl of ice cream.
Despite all the attention given to it, milk allergy is not very common. One to three percent of infants will have it, and most will outgrow it by the time they are two or three years old. The symptoms that can be seen with milk allergy include: diarrhea, vomiting, abdominal pains, hives, or a skin rash like eczema, cough and wheezing, and poor growth due to malabsorption. Rarely, a severe reaction called anaphylaxis can occur in which the body goes into shock.
No one is entirely sure why some children have allergies and others don't. There appears to be some genetic component, as food allergies in one family member often indicate that others in the family will have it. Other things such as infections and other illnesses probably play a role in why some children develop an allergic response to a particular food.