I’m so sorry that your recovery sounds rough- it does sound as if your vagus nerve has been irritated by the surgery or post-op swelling, these are typical vagus nerve irritation symptoms. If you want a good explanation of these effects, @GrnyAny did a really detailed post, here’s a link to that:
Successful Surgery for severe Vagus Nerve Compression - General / Eagle Syndrome Stories - Living with Eagle
Unfortunately because you’ve not been able to take time off work, this could be inflaming the surgery site & setting healing back, so it’s a difficult situation…
Looking at your post-surgery CT, it doesn’t look as if anything was taken off the styloid at all, it looks (comparing it to the remaining side) as if it’s just the calcified ligament which was removed. So it may not be enough to stop any jugular compression, although we can’t tell from this image; if the jugular was being compressed between the C1 process and the styloid then hopefully the IJV should have more room as the styloid isn’t past the C1 process. It’s still early days for healing really, so there’s still plenty of time for things to improve, so hang in there, praying for you 
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