Respect is earned. Sex is irrelevant. It's not like you went on a date and told people you slept with her. You were engaged in an argument in which you were equals. It sounds like she disrespected you.
You can take so many times, but that is the point of being in a professional work environment. You act professional unless your life is in absolute danger. You don't stoop down to their level, otherwise you're going to look just as bad as them. Fighting fire with fire is ridiculous. You took the bait and as a result, now you look just as bad as she does.
That's unbelievable, they're both incredibly moronic. One might normally pity the oversensitive one, but when a dipshit cries for no reason then tries to blame it on you all sympathy probably goes out the window.