You never HAVE to go to a wedding, no.
But don't expect your sister to be on good terms with you if you skip her wedding.
Go to therapy and also see your doctor for medication.
Realize that the wedding isn't about you. If you attend and make it a point to appear unhappy and uncomfortable, that's shifting the focus to you. Otherwise, if you don't make it a point to draw attention to yourself then nobody is going to notice you.
If you truly feel that you cannot manage it, speak to your sister ahead of time and explain the situation. Don't just RSVP "no" - or worse yet, say you'll attend and then ghost at the last minute - and leave her hanging.
If she's aware of your personality/condition maybe she will understand. Or maybe not. IDK. Talk to her and see. But, again, whatever you do, don't make it about you and your anxiety - it isn't your day. Do what you have to do, but don't center it around yourself.