How can I tell if my 1 year old son is allergic to whole milk?

Remove from diet. Milk allergy can be subtle and does not always show up on acute testing. A good way to determine is to remove it from the diet for a month or so and then reintroduce it. In general milk has some issues...Pesticides, recombinant growth hormones and can be allergenic for many people.
Allergy. He may have uncontrollable vomiting, blood in his stools, eczema or even hives. If you suspect this you should see your pediatrician. Allergy testing may be helpful.