I hope the vascular surgeon recognizes the gravity of your need for a styloidectomy since your styloid is affecting your carotid arter(ies) on that side. Getting the pressure off that artery should go far toward stopping the TIAs. It is critical for the styloid to be removed as close to the skull base as possible so that’s another topic to discuss if he says he is willing to operate.
Here’s a post about surgery that @Jules wrote that has a lot of helpful information including questions to ask a doctor you may be considering to do your surgery: