anesthesia is a drug used during any type of surgery
Some factors are needed to answer this question, such as, dose, type, with or without epinephrine.
I am in the Dental field. The first thing I would ask you is if you were under general anesthesia or local anesthesia? If you were under general anesthesia than your throat probably hurts because they used endo-tracheal intubation. If you were only under local anesthsia than it is quite common to have swelling and sore throat after extractions, especially the wisdom teeth. Did your dentist give you antibiotics to take afterward and post-op instructions?