Use moist heat ie. heat a wet towel in the microwave. Tylenol is for nerve pain, Advil for inflammation. You can alternate. You may need something stronger, however, and some of the stronger meds are expensive.
Go to your medical doctor and describe it. It could be nerve related, not a tooth problem. However, because it has changed sides, I'm not sure. I was going to say Trigeminal Neuralgia. Look that up. But it doesn't change sides unless you have it on both sides.
It really does sound like TMJ. Can you try sleeping with a mouth guard and see if that helps?
You can also take something to reduce the pain.