Yes stress and even anxiety can cause a sharp pain in the head.
When you have sharp pains in the head it might feel like you're on your way to a stroke or aneurysm but it's usually no cause for concern.
A few years ago I was also experience some sharp pain in my head that wouldn't go away so I went to urgent care and had it checked out.
Turns out my blood pressure was too high and was a result of being stressed out too much over work so yes if you're stressed out constantly your blood pressure can rise and then lead to sharp pains in your head.
If you've calmed down and gotten less stressed and your blood pressure is okay but the sharp pains continue in your head then you should have it checked out just to be sure it's nothing else serious.
But most times the sharp pains in your head are caused by anxiety and stress and is just a way of your body responding to the elevated stress and anxiety.