I agree. Sometimes you can only be human and that includes acting rashly or blowing up.
You could always apologize for blowing up.
Not the funnest idea but if you are upset about it, it may make you feel better. Or you could move on. Personally, you both threw some low blows and were both wrong. Ultimately though I think both women were pretty out of bounds. The first one for starting it all and the second by being shocked at you blowing up at someone because of their gender.
Respect is a two way street. Yes, men should treat women with respect but that doesn't mean that women get to do as they please.