Hi Dersen,
Welcome & thank you for posting your ES story & the images. It looks like the surgeon you saw did a great job of cutting your styloid back to the skull base on the left side so it is not longer involved w/ the IJV compression. The TPs of C-1 look to be the main cause on both sides as your right styloid, even though still intact, is angled away from C-1 & doesn’t appear to be part of the IJV compression on the right (I could be wrong here especially based on the info you gave above about how much space is between styloid & TP of C-1). The muscles involved in compression would most likely be the SCM, but I recall there are others in the area that can also be a problem. I think @KoolDude has commented on that regarding another member’s CT images in the past.
Your right IJV appears to be dominant & thus drains more of the blood from your brain than the left. Many doctors assert that the human body only needs one working IJV to function well. Some of our members who’ve had bilateral compression, as you have, would disagree w/ that as they have found they feel much better after both are open & flowing.
The extra veins you see are most likely collateral veins that have developed on the left to help drain the de-oxygentated blood from your brain as your carotid arteries pump oxygenated blood in. It’s common to see these in people who have severe IJV compression.
I"m sure it’s discouraging for you that your surgeon is out on paternity leave for two months so you have no one who can really provide you w/ good medical answers. It seems resolution may require shaving of the TPs of C-1 to make more space for the IJVs, but it’s also possible there are other less invasive approaches since there are muscles involved, too. I can’t tell from your images how your cervical spine looks, but many of our members have “military neck” i.e. the lordotic curve is gone from the C spine. There are exercises that can be done to restore the curve. Here’s a link to one discussion on this topic, but there are others. @vdm did a lot of research on this & restored the lordotic curve to his C spine: "Military neck" (loss of cervical lordosis) relation to Eagle's - the missing link? - #5 by Isaiah_40_31
Do you mind telling us who did your surgery? If he’s not on our Doctors List, I will add his name.