I faced the same problem with my tooth. I find no results using antibiotics Finally I followed a home remedy that helped me to reduce my tooth pain.
i.e. Put a few drops of tea tree oil in a glass of lukewarm water and rinse your mouth with that solution. You can feel an effective pain relief.
Thanks for sharing....
If the tooth is dead i.e. necrotic, then I would think that a root canal would be an advisable procedure. I had a necrotic tooth and an infection in my gum, an infection which did not clear up until a root canal procedure was performed.
Going back to your dentist to have further treatment is advised.