Anxiety is such a hard thing…it could partly be as @Andy89316 says, using your muscles with speaking etc, (many members find that speaking is something which aggravates their ES symptoms), but also a muscle tension thing if you are anxious- any muscle tension in your neck or shoulder can cause pain, and anxiety can cause that pain in the throat feeling, like when you’re trying not to cry? This post by @Skatkat might resonate with you:
Need to come clean…will anyone else…? - General - Living with Eagle
The styloids can irritate the vagus nerve too, which can also cause anxiety- is this a recent thing for you or have you been anxious a long time?
The surgery does have risks, and can be a tough recovery for some, so should be something you think seriously about…if you have symptoms worse when you’re anxious then maybe it might be worth getting some help with that & see if you can make symptoms bearable first before having surgery? Of course if you have other symptoms which are difficult to live with then that’s different…
Sending you a hug 
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