Confession time🙂
I've been a socially anxious person all my life (though I doubt its severe enough to be classified as a disorder).
I hated interviewing for ages because of this, even though I outwardly wasn't TOO bad (I still usually got hired), I still despised it. I was the kid that never spoke up in class, I'd wait til afterwards to ask questions, even for much of college.
Practice makes perfect. What did it for me was going on TONS of interviews, even for jobs I had no intention of taking. Apply at grocery stores, delis, the mall, etc. The questions won't be the same as grad school (obviously) but you get used to answering questions, and it doesn't cost you anything other than time.
Its what I did and I have gotten much better, and I now have more troubles in "social" situations then at interviews. I'm more comfortable being interviewed by 3 people with doctorates about my research than I am talking to college kids at a party😉 Typing that I realize that sounds kind of sad.....but it sure was great when I went on grad school interviews! Keep practicing and you'll get comfortable with the process. Depending on where you apply, the interviews may end up being very low stress and not a problem anyways (mine sure did).