Are milk allergies common?

Yes. Somewhere between 2-5% of children will have a milk allergy. Many but not all will outgrow that allergy as they get older. By adulthood only 0.1-0.5% of people will have an allergy. However, milk intolerance (lactose intolerance) is extremely common in adults. While not a "true" allergy, it can cause gas and diarrhea when milk is drunk. This happens in 25% of caucasians and 90% of asians.
Milk allergy. It is one of the most common food allergies in children. Fortunately most children will outgrow this allergy between the ages of 8-12, and sometimes sooner. This is very different than lactose intolerance.