I’ve been struggling with chronic pain for almost eight months. It started when my orthodontic treatment caused the root of one of my teeth to break—it had already been weakened from a previous injury. The extraction was straightforward and only took 10 minutes, and I had an implant placed (with a temporary crown attached to my braces). Healing went smoothly, and the CT scans looked fine. But soon after, I developed…
The pulp in the teeth are quite sensitive and can inflame easily, and that inflamation has nowhere to go (being bound by the hard sides of your teeth and jaw), which can lead to constant pain. I once had a routine filling that took about 3 months to stop aching and I had to take ibuprofen every day during that time to be able to focus. Per the dentist, constant aching pain = it's slowly healing, leave it alone. Sharp intense pain = pulp is dying, need root canal. Granted, this is pain the mouth and not in the head like you described.
If it's been a while and it's still bothering you, I'd definitely consider having it removed too. It would suck to remove it and still have the headaches, but at that point you can start looking at other causes.