Re: allergic to breast milk?!
There is a really rare metabolic disorder called galactosemia that is part of the newborn metabolic screen. It is an inability to digest galactose, so babies with it can't tolerate milk from any animal (mother's milk, cow, goat, etc.). They have to be fed soy or amino acid formulas. (Galactosemia is not the same as lactose intolerance.) So it's possible that her baby has galactosemia, in which case he truly is unable to tolerate her (or any other mammal) milk, and there is a test for it.
You can have allergy testing in babies and toddlers done, but is kind of controversial. Some will tell you it's completely unreliable, some have gotten good information from the testing--sometimes it reveals allergens that make their way from mother's diet to breastmilk and cause a reaction in the baby. Dairy is a really common allergen like that, but so are soy, wheat, and nuts. If you can identify the cause of the reaction, often the mother can eliminate it from her diet and baby tolerates her milk much better.
Catherine, mama to Preschooler Girl 9/08, Toddler Boy 3/11, and Twin Girls 2/14!