Why are migraines so painful? How is a headache sensed?

From my understanding, (a) the brain has no nerves, which is why you can talk to people while doing brain surgery on them; and (b) headache is caused by blood vessels constricting. Now, I am unsure whether migraines are also caused by blood vessels constricting, but in any case - what is it that is doing the sensing of this pain? Or is it a(nother) case of the brain just making shit up because it hates me?