Swelling present even after extraction of abscessed tooth. Will antibiotics help?

Hi doctor,

I had an unusual feeling about a month ago. I did not think anything serious was going on. About a week ago, I began experiencing pain on the left side of my mouth. A few days later, I noticed significant swelling near my jawline under my eye. I went to a clinic and the dentist determined from the x-rays that top teeth inside my jaw had broken, so he extracted them. He also saw that a bottom tooth is decaying and will need to be removed. He said not to expect any miracles regarding the decreasing of jaw swelling. He reiterated that it would take time for the infection to leave my body. I was prescribed Cephalexin, Metronidazole, and Hydrocodone as needed. My question is, when will I begin to see the swelling go down? I am on day two of taking antibiotics. By taking the antibiotics, will this reduce the infection? Also, should the dentist have just drained the abscess? The dentist did not suture after extracting the tooth. Is it always necessary for a dentist to do this? Will the antibiotics prevent sepsis or cellulitis from occurring?