hey, welcome to sas.
in answer to your first question, i think it's going to come down to the relationship you already have with your parents.
My mother has known about my "difficulty" with people for as long as it's been there, even before it had a name, but we're fairly close. I finally told my father last year, but mostly for myself, and my own peace, because i know he doesn't-- and even can't
-- understand what it is like for me. He's a very different sort of person.
However, I'm sure you wouldn't be considering this if you didn't think your parents would care.
In that case i would suggest something like this:
find a moment where it is convenient to talk, let them know you have something going on you want to discuss, then explain what your experience has been like and why you think you have an anxiety disorder. tell them what you want them to do about it, be it support or trying to find some kind of therapy. it's quite possible they will feel helpless, so telling them what you want from them will let them know there's something they can do.
but that would be my standard advice, i don't know you, or your parents, and what would be more appropriate if the circumstances are different than i imagine from your post.
best of luck