Is the fast of one who was compelled to drink medicine at the beginning of the Fajr Adhan valid, or must she fast two consecutive months?

One must abstain from things that break the fast at the advent of true dawn, not upon hearing the adhan (call to prayer), due to Allah’s saying: "And eat and drink until the white thread of dawn becomes distinct to you from the black thread [of night]. Then complete the fast until the night." So, if the adhan was before dawn, the fast is valid. But if it was at dawn, the fast is invalid, and a make-up fast is required, unless you believed that the muezzin was calling the adhan before its time and it turned out otherwise; in that case, the fast is not invalidated.