I also wondered if what you have is migraine related. I also get those continuous headaches and have found a visit to a physio really helpful, especially one who is good with necks. Mine usually happen when I'm stressed or when my shoulders are bad, seemingly when my shoulders are bad the neck tenses up to compensate, so even though I don't have a sore neck as such, I get those pre migraine headaches.
I've been prescribed with a fast release "immigran" which stops it immediately.
Anyway How are your shoulders?
Just a thought. The physio has given me stretches which help too and he massages and stretches my neck and it settles it down for me to stop the recurrence.
Best wishes, golitho