。
She was so furious she lost herself.
Literal
She [topic-は] rage [out of excess of-のあまり] self [object-を] was-forgetting.
Two pieces of literary register collide here. ~のあまり attributes the consequence to an excess of some emotion or state — 'out of (too much) X' — and reads as more elevated than the everyday ~すぎて. 我を忘れる ('to forget oneself') is a set phrase for losing all self-control through emotion, often anger or grief. 我 is an old, somewhat literary first-person pronoun — barely used in conversation today, but anchored in fixed phrases. The auxiliary ~ていた frames the loss of composure as a state she was already in.