Is it possible for a toothache to get even worse after taking antibiotics?

YES: If you have an apical absess building up pressure in your tooth root you may need a root canal.

Yes: It is possible that the antibiotic is in-effective for that particular situation and another antibiotic needs to be prescribed. Sometimes two antibiotics need to be prescribed based on the infection. The cause of the pain needs to be ascertained by the dentist so the appropriate mode of treatment can be administered.

Yes!: Either repeated taking antibiotics and failing to get treatment, creating more immune bacteria or prescribing an ineffective antibiotic or taking the medicine without immediate followup could all be reasons why a toothache might be worse with antibiotic therapy. Don't delay, see your dentist ASAP!

Definitely, yes: The reason why your tooth still hurts is antibiotics are used to control the spread of infection and does nothing for pain. Painkillers will help control pain, but when the nerve of a tooth is damaged, nothing short of a root canal or extraction will help. See your dentist for evaluation and treatment ASAP.