Hi & welcome!
Your styloids show up really well in your x-ray, I’m sorry that I’m not good with technology or I would label them for you! Your right styloid (left side of the picture) looks quite jointed- that’s commonly seen when the stylo-hyoid ligament calcifies. It’s longer than average and is angled inwards, so that could well be enough to cause symptoms. Your left styloid, on the right in the image, is also long and angled, & it has quite a kink in it so that could well be irritating nerves…It looks like it has ‘joints’ in it too, so possible the ligament is calcified both sides.
Certainly looking at the images it’s worth pursuing ES as a possible diagnosis, so getting a CT done will be good. Is the neurologist aware of ES do you know? If not we suggest that you get a print out of one or two research papers which show that TN and GPN can be caused by ES, or trying to get a referral to a doctor experienced with ES.
Have a look at @CoHDa’s x-ray image, you can see the styloid on the right side of the pic:
My Panoramic X-ray and CT - General / Eagle Syndrome Stories - Living with Eagle
I can’t find any others that have been labelled for you to compare yours with, hopefully one of our members who can do this for you will show you!