She did nothing but call me.

Literal

She [topic-は] me [to-に] phone [object-を] place [nothing but-てばかりいた].

The pattern ~てばかりいる expresses persistent, often excessive engagement in one activity to the exclusion of others — usually with a tinge of complaint or exasperation. Here the past form ばかりいた frames the speaker's perspective as 'all she ever did was call me' — a backward-looking grumble. 電話をかける is the standard collocation for 'make a phone call,' literally 'to apply/hang the phone' — one of many uses of かける with abstract objects (時間をかける 'spend time,' 迷惑をかける 'cause trouble').