Is there any blocked arteries in the brain like a carotid artery that would show on ct?

Yes. Cta is a good test to evaluate the vessels of the neck and brain. You can have blockages in the vessels inside your head.
CT scan. CF scan is initial scan, if suggestive of blockage, MRI follows.
On CT Angiogram. You must have intravenous dye with ct scan which is called ct angiogram to evaluate blocked arteries like carotids.