Glad to see, you are making a rapid recovery in terms of wound healing. As you guessed, it is probably swelling that is collapsing the thin-walled IJVs.
Here is @M_UK who went through both Styloidectomy and C1 trimming in UK by Dr. Axon just like you. He did an excellent comparison Pre and Post surgery IJV flow 9 months afterwards. He quantified it using computational fluid dynamics.
We also discussed it here after 5 days of his surgery. It also includes links to studies of neck operations and IJV narrowing as result of it. Kinda gives you perspective on what to expect. Hang in there. You need at least 3 months to assess it. See the study in the link below.