Yes, most certainly TMJ can cause headaches without a doubt. I had severe right ear pain for 4 months before I was properly diagnosed with TMJ...no medical professional was even looking at that. I had a brain MRI b/c of TMJ but that was for ruling out a brain tumor.
My friend was out for dinner, with her husband enjoying her meal, and suddenly she could not close her mouth. Very frightening. She directed me to her dentist. My feeling is you need to see a specialist in TMJ disorder. Not a general or family dentist. I had a very involved work up with her for evaluation. And then was fitted with a dental appliance unlike I had never seen. Very difficult to get use to at first...wearing it at bedtime only. The top and bottom are "connected" and once in your mouth you literally can not open your mouth at all. When they first placed it in at the office, I felt panic which they understood completely. It's a scary feeling but you do get use to it. I wore this for 1 year and gradually my mouth/jaw was able to open bigger and bigger and the right ear pain vanished. And it was expensive. I now have Invisalign liners from my general dentist. I have an very bad overbite and my 2 front teeth were sifting. I can see my teeth already moving in the right direction and hope this will keep the TMJ pain at bay. Also I found heat to be better than cold for TMJ/ear pain. I know folks who wear their TMJ appliance for the rest of their lives. I am giving Invisalign a try and so far so good.
Best of luck to you!