What Are the Signs & Symptoms of a Milk Allergy?

In children who show symptoms shortly after they have milk, an allergic reaction can cause:

wheezing
trouble breathing
coughing
hoarseness
throat tightness
stomach upset
vomiting
diarrhea
itchy, watery, or swollen eyes
hives
swelling
a drop in blood pressure causing lightheadedness or loss of consciousness
The severity of allergic reactions to milk can vary. The same child can react differently with each exposure. This means that even though one reaction was mild, the next could be more severe and even life-threatening.

Children also can have:

an intolerance to milk in which symptoms — such as loose stools, blood in the stool, refusal to eat, or irritability or colic — appear hours to days later
lactose intolerance, which is when the body has trouble digesting milk
If you’re not sure if your child has an intolerance versus an allergy, talk to your doctor.

https://kidshealth.org/en/parents/milk-allergy.html