Hi there,
Our son is 14 months old (on the 7th) and he was diagnosed with dairy, egg and peanut allergies last month through allergy testing. You should mention your suspicions to your pediatrician, really.
Davey, our son, wasn't throwing up when we tried giving him dairy, eggs or peanut butter. Instead, his skin would get really red around his mouth, neck and down his chin, or wherever the food touched, and then little water blisters would appear. This would happen within minutes of exposure to the foods and would disappear within 20-30 minutes. When we described this to the pediatrician at the 1-year well-baby visit, he said he wanted us to avoid those foods and set up an appointment for testing with an allergist.
Anyway... You can test for sensitivities pretty easily by putting a little of the suspect foods on your baby's skin and monitoring his reaction. Kind of a do-it-yourself allergy test. Just put a dab of the food (i.e. milk or yogurt) on your baby's cheek or back and see if he develops a rash.
As a side note: babies need full-fat, not low-fat dairy (or non-dairy substitutes). You should avoid using low-fat.
Good luck!
J.