Thank you for your question and welcome to Just Answer.
Your dentist has been remiss in ignoring this abscess just because it tends to drain and keeps the pressure and the pain at a minimum. A chronic draining abscess slowly dissolves the bone from around the roots of the non-vital tooth and eventually creates quite a cavern of pus inside your jaw. For some reason the drain has closed off and the pressure is now building. You have to insist that your dentist treat the tooth or have it extracted, but not until you get the pressure to come down first.
You need to be placed on antibiotics, and that will require a prescription. Call your dentist's office and have him call one in for you and start taking them today. It takes 24 to 48 hours for these to start taking effect, so the sooner you start the better.
At home, you should start rinsing with hot ( as hot as you can stand without burning yourself) salt water. Dissolve one teaspoon salt in 8 ounces of hot water. RInse over the abscessed area for two minutes and repeat every 20 minutes. The heat from the water will soften the abscess and encourage it to point, not unlike a pimple, and burst, relieving the pressure.
I hope this answers your question. If you would like to discuss this further or have any additional questions, please reply to my answer and I will get right back to you.
Sincerely, ***** ***** DDS