Hi & welcome!
There have been a few, very rare cases of styloids causing strokes, it can happen if they compress the carotid artery. It sounds from your symptoms as if the styloid is compressing the IJV, which can cause raised intracranial pressure, the clogged ear feeling is common with that. (There’s more detailed info about vascular symptoms in the common symptoms & possible explanations section) So it does sound as if you have vascular ES, as well as possible nerve pain.
If it was me I would postpone the jaw surgery, and try to find a doctor with experience to get an opinion. We’ve had quite a few members who’ve had dental surgery which has really increased their ES symptoms, possibly from all the pulling & tugging on their teeth? So from the sound of your jaw surgery, this could potentially cause quite a flare in ES symptoms. Depending on the angle of the styloids, it could potentially move them into more contact with the blood vessels, although that’s just a guess, I don’t know for sure, but having ES surgery sometimes has altered people’s jaws so that they find if they have a bite guard it doesn’t fit properly afterwards, so it could happen the other way round too? 
And your concern about swelling is a valid one too, so I would certainly want to discuss this with your jaw doctors, it needs careful thought.
I’m not very good with tech stuff, I don’t know if these are any help to you with your imaging:
Making Your Own 3D Images from CT Scan- 3D Slicer Tutorial - Living with Eagle
RadiANT DICOM Viewer tutorial - General - Living with Eagle