Welcome to Just Answer and thanks for your question. If a strep test was all that was done (rather than a throat culture to look for any type of bacterial infection), then the throat can be infected with another type of bacteria (other than strep) from your tooth or other source. You may also have a viral throat infection that isn't connected to anything else at all. If that is the case, then your immune system will clear it on its own since antibiotics don't work on viruses. Any antibiotic the dentist starts today should help before Friday if it is bacterial.
A viral infection can last that long. If it were a bacterial infection from the tooth, the bacteria would have shown up on the throat culture.
Tonsils are lymohoid tissue and can swell from any kind of infection in the area that they drain. It is possible that the swelling is from that, but impossible to say with certainty.