You sound as bad as each other to be honest. Clearly both of you have some growing up to do - and the only way you'll both do that is if you just cut all contact and learn from the experience by yourselves in your own time. Maybe in a few years when you've both grown up a bit, moved on and have full closure on it - you should think about getting back in touch as friends but other than that... You're both just perpetuating some stupid little game where you can both be vindictive to each other for self-deprecating kicks.
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I feel you... She should respect the fact that you're having a hard time dealing with it and keep away from you until you make the call to be friends. Dumping someone and then actively pursuing them for friendship whilst emotions are raw is a dick move.