A food allergy is an immune system reaction to a food. MedlinePlus lists cow's milk among the foods that most often cause food allergies.
Symptoms can include hives, vomiting, stomach cramps, or swelling. In rare cases, a food allergy can cause a life-threatening reaction called anaphylaxis.
The only way to prevent a reaction is to avoid the food. Read ingredient lists and follow your clinician's advice.