What would cause spasms in your neck or carotid artery?

Carotid spasms. Carotid spasms occur only with direct manipulation of the artery itself, such as during an operation or during a catheterization. Carotid artery spasms will not cause pain that one would attribute to the neck in any way.
Poor posture . Muscle spasm from posture, & exercise are not uncommon. Carotid spasm is rare.