Try rubbing your head with an ice cube for several minutes. On a side note, I could be wrong, but I would see a doctor; it could be an underlying medical condition, i.e. hypertension...
I've never experienced headaches as a result of head shaving, so it's kind of hard for me to imagine that one would cause the other. Is it possibly an allergy to your shaving soap or cream?
It's possible I guess. Try a different razor without the lubricating strip.Do you have any issues when shaving your face with the same products?