If she's a total head-fuck then move on bro!
Don't beat yourself up too much about it. You haven't 'fucked up', she's just a head case. Even if you suggested a date she may well have flaked. It sounds like she uses guys to make herself feel good and serially does this.
That said, you're a bloke and you wanna just shag her irrespective of her saddo personality. I get that
Let some time pass (a week, two weeks whatever!) and let the old wounds heal. If she hated your guts she'd have removed your ass off her friends list on FB.
After some time has passed initiate contact again...and start from the beginning
In the meantime concentrate your energy on getting out there and game other girls. You'd be amazed how quickly you'd forget about this one when the next HB comes along
