They won't take it out while it is infected, for fear of introducing the infection to the extraction wound and thence into the bloodstream. Sepsis is a danger. That has to be dealt with first, then the extraction. That is why she needs to either return to her own dentist or go to A&E.
Personaly, I would think that after two different antibiotics have failed to control it, a really strong intravenous AB will be given and she will be kept in and closely observed. This is exactly the worst time of year for it, but the alternative just doesn't bear thinking of.