I think from reading many members’ experiences on here that blood pressure issues & tachycardia are more often from vagus nerve compression/ irritation, but you’re right that if the carotid artery sheath is affected by the styloids this can cause heart arrythmias too. Often if the carotid artery is compressed you’ll get dizziness, fainting, headaches too…
@GrnyAny did this really helpful post about her symptoms:
Successful Surgery for severe Vagus Nerve Compression - General / Eagle Syndrome Stories - Living with Eagle
And there’s some info in the Newbies Guide Section about symptoms & possible causes:
ES Information: Common Symptoms And Possible Explanations For Them - Welcome / Newbies Guide to Eagle Syndrome - Living with Eagle
The best way to see if the blood vessels are affected is with a CT with contrast, but if you’ve just had a CT that would mean exposure to more radiation, which isn’t ideal. A FIESTA MRI can show nerves at the skull base, but they’re not done in many places, we’ve had some discussions about that & very few members have had them.
Unfortunately for alot of us the only way to see which symptoms are being caused by what is to surgery, unfortunately! I’m sorry I can’t be more helpful, let us know what the CT shows when you get the results 
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