The verb aḥrama can indicate entering a state associated with sanctity. In this occurrence, the expression signifies entering a sacred month. Reading every occurrence only as the pilgrimage state of iḥrām would misrepresent this narrative.
Fa-aḥramnā is first-person plural past; thumma milnā marks sequence. Wa-fīnā banātu qawmin imāʾ describes the accompanying circumstances.