Ok, read all the other replies and with what you have said, there are plenty of ideas here. Anything beyond that would require developing all the participating characters further.
I like what @DokiDokiTsuna has said, for everything that matters to Nasty, there can easily be a secret behind it that will hurt her. In fact, it would make sense that what matters the most to her (Nasty) is what she is lacking, and why she is putting such an emphasis on it.
Extra points, if what she is making fun of (that this schoolmate has) is actually her biggest fear as well, as it is her reality that she has not shared with anyone.
Double-Extra points if this issue also bothers Goth girl, or can be related to her in some way, so it forces a confrontation and realization/acceptance of her own situation at some point in the story down the road. That way this isn't just a small subplot, it actually also matters to your story.
See what I mean about further character development? I have to start building each character to make this work with whatever I come up with.
So here's an idea that instantly popped in my head, and it built off what @DokiDokiTsuna suggested.
I really liked Nasty being adopted as an idea for some reason. And what the Goth girl spay paints on her locker is the last name (or first name even) of her real mother. This would probably mean nothing to everyone else in the school, but everything to Nasty. (Of course, all this assumes that Nasty is aware she is adopted, knows who her real mother is and is trying to hide it.)
I could go on all day about this or other scenarios, but yeah, it means I build the characters as I want to so they can fit the story, but that wouldn't be right. These are your characters, and your story.
I hope this helps you.