Translation:I broke up with my girlfriend last year.
Yes in that とdoesn't imply who intiated it, but I feel that the は does.
*I suppose an arguement exists that it should be 去年は instead of what I wrote, but it felt more natural to me to leave the 去年 alone to mark the time and to put in 私は through an ellipsis.
°If the sentence wanted to leave it vague as to who did the breaking up, I feel that it would have been written as "私と彼女は" instead.
It's わかれました, which according to Jisho.org can mean:
- to part (usu. of people); to part from; to part with; to be apart from
- to separate (of a couple); to break up; to divorce
- to lose (e.g. one's mother); to be bereaved
So while it doesn't apply only to romantic breakups, it is limited to different kinds of partings between people rather than breaking for example a twig.