As far as I know, headaches can last anywhere from a few minutes to a few weeks. It's not normal to have headaches at all, so no, it's not normal for you to have a headache that lasts for a week. But as far as headaches go, having one for a week is not unusual. Have you seen a Dr about it? I hope you get it figured out and get some relief soon. Take care.
I've had a full blow migraine for 9 days before it turned into a hard throbbing headache that lasted another 7 days. Over two weeks! Under this time though ( after day 3) i was monitored by a Dr. HOpe you find some relief.