。
She got it into her head that I was talking behind her back.
Literal
She [topic-は] I [subject-が] her bad-mouth [object-を] is-saying [quotative-と] thought-and-stuck.
思い込む is a compound verb: 思う ('to think') + 込む ('into') — literally 'to think one's way into' — meaning 'to be convinced of, to assume strongly,' often with the overtone of mistaken or unjustified conviction. Adding ~てしまった layers in regret or finality: 'she ended up convinced (of something untrue).' 悪口を言う ('to speak ill of, to bad-mouth') is the standard phrase for talking behind someone's back. The whole sentence captures the social trap of being misjudged.