Hello andwoo,
what a complete and utter bummer about your headaches. When I get headaches, they are totally disabling so I really feel for you.
You mentioned that you were -
"diagnosed with a very rare headache disorder, new daily persistent headache, of which they know very little about, know next to nothing about why it suddenly starts in people for no reason."
yes, tmj causes nasty headaches and nausea, but I would be more concerned about what the neurologist says is wrong with you and how he/she is going to treat these headaches.
Tmj headaches tend to mimic migraines in that the pain can be focused on one side of the head in the temple region. My family doctor was so positive that my headaches were migraines and tried treating them as such, but nothing worked. I knew that most were tmj headaches because if and when my tmj relaxed, I could feel the headache go away. Yes! Once my tmj became more manageable, the headaches went away except for those irritating monthly female ones.
I would get more information from your neurologist if I were you. Get a name or something and then start researching over the internet if he can't give you info.
With your jaw clicking, you probably do have a case of tmj. It wouldn't hurt to treat your jaw like it does and see what happens. By that I mean - be gentle with your jaw by eating only softer foods, no gum or ice chewing, particularly don't eat anything chewy or hard. Baby your jaw by not opening it wide. Try talking less. Look at how you hold the phone when on it. Don't hold the phone with your shoulder. Bad. Use lots of moist heat directly on the jaw joints. Try and relax the tension in your shoulders. Keep your teeth apart with the tongue resting on the roof and the lips either together or slightly apart. Teeth should never come together (except maybe to eat). Posture is another area where you should seriously evaluate what you are doing. Check out the tmj physical therapy page at nismat.Org for basic info, pictures, etc.
Some anti-seizure medications do help tmj so if it is helping - great! Medications for tmj is an interesting subject and since people are so different, the meds all seem to work differently, so patients do a lot of experimenting (always doctor supervised though).
Take care. I hope you'll keep us informed as to how you are doing. I hope and pray that the docs will be able to help you.
God bless...
Carol