Now that my husband and I are done laughing hysterically, I'll share our results.
My husband, in perfect health, has absolutely no swelling around the bottom of his neck no matter how long he holds his breath and bears down (and it was a long time). I have MS (not tested for CCSVI yet), and when I do the same, the hollows at the base of my neck immediately fill and swell slightly and the veins above begin to swell out. Both sides, left more than right. Not as pronounced as yours, Eve, but definitely present.
I wonder if some of the difference could be due to our neck structure. His is thick and muscular and could hide the veins pretty well. Mine is more "elegant"

and can't hide much. But there is most definitely a difference in what appears to be blood drainage (or lack of it) while holding one's breath.