@inhomecaretx,
In light of extensive case studies performed by people in the previous 4 to 5 centuries, into this perplexing issue, headache is most commonly down to external stimuli.. secondarily, closely followed, by internal convergence of factors.
In your case it appears to be the latter, some internal chemical or neural issue is causing the morning head. I would be so bold as to suggest it was circulatory in nature as a first point of thought, perhaps you sleep with your head raised too high or too low?.
Perhaps consult your doctor if not, also check for no hums or vibrations in your room at night, notice any frequencies?.. IE: a junction box for electricity outside?.
If one imagines the pain transferring to ones cat, who one rests ones head on gently, one does find some relief. (he said jokingly).
But seriously, you can use brain power to discharge a fair bit of pain if you can 'believe' it, I had headaches for a while and imagining it transferring to the bed post seriously did fix it. The divine comedy which is 'frog on head' is actually rooted in some degree of psychological truth.