@jenlink- I remember hearing about Eagle's Syndrome but never knew what it was. I do now, sort of... From what I gather it is indeed very rare and very difficult to diagnose. It is an elongated styloid process. The length of the styloid process is usually 2–3 cm [2]. When it is more than 3 cm it is called an elongated styloid process, and it can cause pain in the throat, difficulty in swallowing, foreign body sensation, carotid artery compression syndrome, etc.
https://www.medicalnewstoday.com/articles/321946#treatment
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4439650/
I am trying very hard to describe this disease but I am not a doctor. "Eagle syndrome is most commonly seen after the age of 30 years. There is no significant sex predilection in the occurrence of mineralization of the SP; however, symptoms are more common in females.[8] Eagle's syndrome is not frequently suspected in clinical practice. The symptoms in Eagle's syndrome range from mild discomfort to acute neurologic and referred pain. These may include: Pain in the throat, the sensation of a foreign body in the pharynx, difficulty in swallowing, otalgia, headache, pain along with the distribution of the external and internal carotid arteries, dysphasia, pain on cervical rotation, facial pain, vertigo, and syncope.[12,18]
The styloid process is a thin, elongated, cylindrical bony projection that is situated anteromedially to the mastoid process. Its length varies from 2 to 3 cm. Posterior to the styloid is the facial nerve, which emerges from the stylomastoid foramen. Medial to styloid, moving posterior to anterior are the internal jugular vein (with XI, XII, X, and IX cranial nerves) and the internal carotid artery. Medial to the tip of the styloid process are the superior constrictor muscle and the pharyngobasilar fascia, which lie adjacent to the tonsillar fossa. Lateral to the tip of the process is the external carotid artery that bifurcates into superficial temporal and maxillary arteries. The stylohyoid ligament extends from the styloid to the lesser cornu of hyoid bone.
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4379291/?_ga=2.36630178.326493342.1582377355-517597283.1582377355#!po=31.8182
Are you seeing a dentist or oral surgeon or head/neck surgeon?