Hi M_UK,
I am glad that you have the surgery and it was success and I am wishing the lingering issues will clear in time. I am not doctor nor do I know what is really causing the new narrowing but having seen many academic papers on neck dissection operations and their impact on the weak walls of the Jugular Veins makes me agree with Isaiah and Jules that it could be post-operation swelling.
My assumption is that since muscles surround the jugular vein they might have been moved or dissected during the C1 shaving/drilling and were stitched back together after the surgery. This can hypothetically cause temporary compression of the weak wall of the Jugular Vein. In the previous CTV, the Jugular Vein segment below the narrowing was not compressed and the pressure outside and inside (intermural pressure) was equal. But if that pressure is somewhat unequal, the Vein can easily collapse and appear narrowed. To put in perspective how weak the walls of the IJV is, on standing up, jugular veins collapse under force of gravity to more than 50% of their supine diameter. So in theory, swelling could exert outside pressure to collapse them significantly.
I hope this new narrowing will diminish as the swelling subsides and the blood flow will improve. Just give it a time. I really doubt that all of sudden something new is compressing it that needs another intervention. Even scar tissue can not compress it that long. Wish you quick recovery!
BTW, I still see the collateral veins are compensating (typical of jugular compression) and not significantly improved after operation due to probably the swelling-induced compression. I also marked light blue lines along where I assume the swelled muscles might be compressing the Vein. Arrows pointing to the Collateral vein.
The picture below is from the internet and hypothetically shows how muscles surround the jugular vein.
Here is table from patients that went through neck dissection who had narrowed jugular vein but the number reduced from 46% to 10% after 3 months.
The study Link : (PDF) Internal jugular vein patency after lateral neck dissection: A prospective study