I’m inept at technology today as well & have to rely on my husband or son for help.
I apologize, I was looking at the wrong structure in the original picture & was focusing on the thicker bony mass to the right of the right styloid. Not sure what that is (not a doctor…). Your assessment is logical - it’s likely your stylohyoid ligament that’s calcified. The right styloid does look thicker than the left but it also looks fairly normal length. In all likelihood it’s the calcification that’s circled which is causing your symptoms.
As far as the surgeon goes, ask to be put on a cancellation list. I’ve often been able to move up appts scheduled farther in the future by a month or more because of cancellations.