Swollen cheek, jaw and gum on left side. Dentist has provided me with amoxicillin and metronidazole. No toothache... What's wrong with me?

Ask dentist. your dentist prescribed antibiotics for a reason. A diagnosis should have been discussed with you. If you don't get answers from the Dr. Who examined you,get a second opinion and diagnosis.
Infection. Your dentist is treating you for an infection. He will have to localize it to treat it effectively.
Need more info. I think that you should ask your dentist since he had the opportunity to examine you and make a diagnosis and therefore is the best person to know what is wrong.