Dear K.,
Louise is probably right: this sounds like a milk protein intolerance/sensitivity. It's not classified as an allergy because it leads to mild-to-moderate gastrointestinal upset, not to the kind of anaphalactic (sp?) shock associated with peanut allergies, and it can't be detected by an allergist's skin-prick test. But please trust me on this: it can lead to serious medical problems. A child who throws up after drinking milk should *not* be drinking milk. (The fact that she had a rash after drinking Lactaid is actually another sign that protein is the likely culprit. Lactose is a sugar that some older children and adults can't tolerate; it's not related to the protein that causes problems for infants and toddlers.)
I strongly recommend two things:
1. Get a doctor's note for WIC so they'll cover soy
2. Consult with another GI! I was actually shocked to hear of such a cavalier response to a child's vomiting -- a milk protein sensitivity can have serious side effects if not addressed appropriately, and vomiting is a very clear signal. You have the right to a second opinion on this one.
Here's some more information on milk protein problems: http://allergies.suite101.com/article.cfm/milk_allergy_or...
Oh, and one more thing: read all ingredients! Many products for young children (teething biscuits, baby toothpaste, etc.) are made with milk powder. Most but not all products list allergenic components in bold at the bottom of the ingredient list (it'll say "contains milk," "contains wheat," etc. If you have a doctor's note about milk, WIC should cover alternatives.
All the best,
Mira
(mom to a wonderful milk-protein-sensitive little boy)