Hi nnnia,
You want a head & neck CT scan that cover the area from the base of your skull to & including your hyoid bone. The styloids & stylohyoid ligaments (if calcified) are best seen in a CT w/o contrast. A CT w/ contrast will additionally show soft tissues & is good if you think you have vascular compression caused by the styloids. The usual victims are the internal jugular vein or internal carotid artery. If you don’t have vascular symptoms then there is no need to have a CT w/ contrast.
Here is a post Jules wrote awhile ago that has good information regarding ES symptoms. It may help you decide which type of CT scan you should get.