That really sucks, man. I'm sorry you're going through it.
RE: your living and work situation, in your shoes I'd apply broadly to anywhere with a research job that you could afford to live alone or with a roommate or two.
Big caveat, if you feel that you need familial support for a while you should just go home and get yourself right first, then focus on doing my first suggestion or come up with a different plan during that time. I doubt anyone on an admissions team would ding you for taking a while off after your fiancee broke up with you. Take care of yourself. <3