What are the symptoms of milk allergies in babies?

In its efforts to fend off the invaders, the body releases histamine and other chemicals, which cause allergic symptoms in the body.

Symptoms of milk allergies in babies include:

Frequent spitting up
Vomiting
Signs of abdominal pain, or colic-like symptoms, such as excessive crying and irritability (especially after feedings)
Diarrhea
Blood in stool
Hives
A scaly skin rash
Coughing or wheezing
Watery eyes and stuffy nose
Trouble breathing or a bluish skin color
Swelling (especially of the mouth and throat)
What are the symptoms of lactose intolerance in babies?
Symptoms of lactose intolerance in babies include:

Gas
Diarrhea
Bloated stomach
Spitting up
Irritability, crying or other colic symptoms
Failure to thrive and gain weight

https://www.whattoexpect.com/first-year/feeding-your-baby/milk-allergy-in-infants.aspx