According to research done at the University of Utah, headaches, including migraines, do not cause cell death except in a very small group who suffer a migrainous infarction. "You're more likely to be struck by lightning,"

Migraines: Do They Damage Your Brain?

Notice, he said the person may experience slow thinking or such for hours to even a few days but this is not from damage.

I've seen similar comments made by other doctors and researchers.

Pain and headaches can temporarily disturb brain chemistry causing changes in how one feels and function. This is no different than feeling weak or fuzzy because one has not eaten. Eating restores brain and body chemistry (metabolism) and normal function returns without any lasting damage.

Anxiety also disrupts proper brain chemistry.