My best friends kids are all sensitive or allergic to milk. The one with the milk allergy throws up after she eats it. The others with the sensitivity get diarrhea after having it. So, yes, it sounds like she has it based on my experience. It can take up to two weeks to get the milk completely out of the system. The other thing to consider is that TONS of processed foods have milk as a component. Crackers, pastas, chips, some soups, cookies, etc.
I would cut out all dairy if you can for two weeks and see how she does. Then add in just whole milk and look for a reaction.
HTH!
Holly