For a 2.5 year old, I'd take the whole family off dairy for a week, and not have any in the house. Then you can just say "we ran out". You could try a rice milk or coconut milk, but I'd actually just give her something completely different. Water would be good. And make foods that don't rely on milk or cheese:
roast chicken with gravy over potatoes
pork roast, roasted veggies
Fry in coconut oil or olive oil instead of butter
Also keep a food journal with all the foods she's eating (and all symptoms) so that if it's NOT milk, or if it's milk AND something else, it'll be easier to tell.
Kathy, mother of 3, wife of 1. My new recipe blog: www.kathysrecipebox.wordpress.com (no longer searchable by allergen, but at least it doesn't have a virus!)