Some common allergens that are in what feels like everything are gluten, milk proteins & solids, dyes, eggs, caffeine, and even some fake sugars can make people violently ill. Until you see a doctor, maybe try a limited food approach? Nothing packaged or process and mainly raw kind of foods (fruits and veggies) to see if there is anything she stomachs. Doubt you can get a 3 year old to eat nothing but salad, but it's worth a shot.
she has not been tested for food allergies. I will suggest that at our next appointment.
Has she been tested for food allergies? If you're finding your pediatrician to be uncooperative, maybe find a new one?