Is this not right? Should I not go out with her?

Okay, Jess is my girlfriend. We've been dating for 2 weeks exactly. But today, my friends came over to hang out, and I was on Facebook. Of course, Jessica says: "hey, we need to talk. Everyone is always teasing me(note that I wasn't teased at all), so I don't think we... should date" I immediately go offline. My friends saw the whole thing, and start laughing their eyes out. Then, they call literally ALL of my friends. I was then getting teased so much. I text-ed her after two hours of pure Humiliation, saying that everyone was teasing me. After two minutes of arguing, she texts me: Fine, I am now dating you. I say okay then, then she has to go... Should I break up with her? Like I feel like shes doing it just so I don't get teased. Or should I stay with her? I like her, but she sounds like she doesn't hate me, but doesn't like me.