Is it possible that my daughter be allergic to milk after drinking milk based formula?

Yes: A person can acquire an allergy to milk at any age. More kids develop transient intolerance to things in the milk. The sugar source, lactose, is commonly a problem after a bad gut virus as a person can lose the ability to absorb it for weeks. A lactose free milk would avoid the issue until the system healed, when it could be used again. Some (1-2%) may have cow milk product allergies for life.