The length of the styloids can be an issue- the neck is a very cramped space with major nerves and blood vessels close together, plus where they exit the skull base is very close to the styloids, so a thick or angled styloid process can compress them as well.
Simple relaxation exercises for your muscles should be okay, but depending on what sort of PT the doctors want you to do, I would be wary- certain neck positions can put the styloids closer to blood vessels (depending on what angle your styloids grow), any sort of traction/ manipulation could be dangerous. You would need a physiotherapist who understands Eagles and knows the risks- one of our members, @Awest , wrote a paper about this, here’s a link:
WESTBROOK et al. (2020) - Eagle’s syndrome, elongated styloid process and new evidence for pre-manipulative precautions for potential cervical arterial dysfunction – Doctor info and research article - General / Research Papers - Living with Eagle
So while I agree with @Mod_support and you’ve been given great advice, there are things to be considered with PT…