@1speechpick Since you complain about the right sided severe headache, I just wanted to bring your attention that Carotid (ICA or ECA) irritation or compression can actually manifest as one sided severe headache as shown below. Also, the lightheadedness you described as if you were about to pass out, is called presyncope that too can be caused by irritation of the either Carotid arteries (ICA or ECA). Even the pain you describe as radiating to the neck and Skull base is called Sub-occipital pain and can be related to Carotid. So I think it is possible that you have Carotid Variant of Vascular eagle syndrome NOT the Jugular Variant. It is also possible that you have Vagus Nerve irritation. Also, your left Hyoid horn could also contribute to this and needs to be tested dynamically to rule out any contact but since you have almost all of the symptoms on the right side, I would like to closely examine your right STYLOID to see if it is irritating your Carotid arteries. Can you please post more images of right Styloid. Axial would be better or even coronal images.
This document is a good read about different variants of Eagle Syndrome. This is where I got the screenshot above.
Source : https://emergeortho.com/wp-content/uploads/2018/04/1-s2.0-S2468781220301399-main-2.pdf
It was also posted here in the research area by Andrea who I believe co-wrote this study.