Hi,
I certainly cannot diagnose you but can just offer up some possibilities.
One is possible trigeminal neuralgia, which is facial nerve pain that can affect your maxiallary and madibular nerves and can cause severe nerve pain in both the upper and lower jaws. It can also cause these pains in your cheeks and lips. There are several medications and injections that can be tried to hopefully reduce the pain.
Another thing that might be possible, which is what happened to my mother, is dehydration. My mother had one-sided severe pains in her teeth and jaw and kept going to the dentist. The pain would come & go, though. Sometimes she had none, other times it would attack like crazy. Her dentist thought it was because she wasn't drinking enough. I personally thought that sounded odd, but she told me she probably wasn't drinking enough. So she started drinking alot, water and juice, and said shortly after her jaw pain stopped. This was a few years ago and I've not heard her complain of it again. So it sounds strange, but I perhaps in her case, not drinking enough really was the cause.
Also, perhaps it could be TMJ related...or even some sort of compression in your upper cervical spine; possible nerve damage in one of your teeth; or some other medical problem that causes those symptoms.
I personally think if the pain is that bad, and seems like nerve pain...and is not helped by painkillers, then it just might be nerve pain. I know painkillers do not help my nerve pains either. I've been taking Lyrica since Feb. for nerve pains all over my body and it does help alot, though I still get some episodes with really severe pain, but steroids seem to help. Now I wonder if you took a Medrol dose pack....if that would help your pain.
If your dentist cannot figure it out, then if I were you, I would try to see a regular doctor to investigate as It may not actually be tooth related.