Abscessed Tooth with Infection

For the past couple of years or so, I have encountered not so severe pain on my back tooth, also the one on the other side..Normally I just take painkillers. Last month, the pain on one side became unbearable and I got that tooth removed.. But from the looks of it, the other unremoved one is worse. The other day I experienced unbearable pain on said tooth and I feel like even my neck is swollen. I went to the dentist to ask if I could have that tooth extracted but she said that I had to take antibiotics for one week and then come back. What if the infection has spread far beyond my mouth? And how do I know if the anesthesia that will be used next week will actually work? Because I've heard of stories that an infection can cause immunity to anesthesia on the tooth area..

[Jerome Tsang, DDS]

Your dentist is probably trying to control the infection.  The antibiotics should help control the swelling and it should, in theory, make the anesthetic work better since the infection would have gone down some more compared to your initial visit.