I'm hypothesizing that she had forgotten your circumstances when she called you out publicly, but once you put her on the spot she wasn't about to back down. After all, this was a face-saving maneuver on her part ("who run bartertown?") and your counter gave her a choice between losing in her mind ("I'm sorry, I shouldn't have made such brash assumptions about what a horrible student you are") or trumpeting her charisma ("I don't care if you have an excuse, I am the alpha-omega"). The dean has far more ability to embarrass her than you do. Invoking the dean immediately solves your immediate problem but potentially leaves her wounded and angry. Giving her a chance to back down has the lowest impact on your future academic freedom. Start with her in private, act contrite, then escalate as necessary. I'm hopeful that you won't need to escalate much.