Most Helpful Girl
Classic manipulative behavior. Sounds like she isn't completely over you and instead of properly dealing with the break up she's trying to cope by putting you down and constantly stating how much better she/her new boyfriend is than you. The best way to shut her down is just... be nice. If you can't do that be civil. Comment on one of those posts now and then saying you're glad she's doing well and that she's successfully moved on. It'll call her out on her BS and she'll realize she isn't getting to you. If/when you get a new girlfriend see how she reacts.
Most Helpful Guy
She clearly still feels for you, and or the relationship you two had togther. She is behaving like a child probably because she can't really understand or make sense of her emotions and the fact that she still feels like she wants you to notice her.
I would say, be nonchalant about her bahaviour, as difficult for you as that may be, it's what you need to do. That will either enrage her, eliciting more obnoxious behaviour, or make her see that you have moved on (you weren't quite clear on whether you wanted to get back with her).
But really, I don't feel sorry for you, I feel sorry for her new boyfriend, because she is clearly thinking about you a lot and not as much about him... DO NOT PLAY ON THAT! Because she will get what she wants, and you will be in a bad place as a result.
If things end with her boyfriend, and she sees the light, and you guys decide to hit it off again (make sure she has broken off from the other guy... doubly sure!), then you need to both sit down, in neutral ground (not in a respective apartment, cause that may lead to just having sex right off the bat), and speak openly and completely honestly about what went wrong in the first place, her bahaviour, and what broke you both up. Leave blame at the door cause it doesn't bloody help; just focus on talking things through, and being mature and honest about the past and why it led to your breakup. Don't let her talk about her side of things only either, make sure that you BOTH lay everything on the table.
Good luck, I hope i've helped.