Combination of stress and movement patters, posture etc. that make callisthenics folks and martial artists look at you with sad eyes. The reason exercise doesn’t help in the moment it’s flaring is because you don’t know how to move. Exercise does help, especially anything that’s training fine-grained full body control and awareness but those are skills which have to be developed over longer time-spans. A good physio might be able to alleviate acute symptoms by poking you in the right way but in the end they’re going to give you homework to figure out your own muscles and bones. Likely some general spinal segmentation exercises with some extra you-specific stuff on top. Also, get that stress under control.
tl;dr: psychological / psychosomatic, not neuronal. The nerves are healthy they’re just carrying BS signals. Blood pressure might be correlated because stressed-out persons don’t tend to have chill blood pressure but it’s not the pressure that’s causing the headache, directly or indirectly, because see what Canadian_anarchist said.