Is it possible that my daughter is allergic to her formula after being on it for four months?

Symptoms? If she has not demonstrated any symptoms after ingestion, then it is unlikely that she is allergic.
Probably not. If she's been on a formula for 4 months and has not developed any symptoms, why would she be allergic just because of staying on it for that long? I strongly doubt. If there's more to the story, please let me know.