I wish I could open up about my anxiety

I've been taking piano lessons with my teacher for about a year and a half, and I still get nervous every time I go. I have anxiety and I am also very perfectionistic and I criticize myself so much when I'm playing the piano. Even if I play a song really well, my brain will automatically go, "Oh you're so horrible at this. You should just quit. You're such a failure." It's worse when I'm playing in front of people. I know I shouldn't be nervous in front of my teacher because she's there to help me not to judge me, and I shouldn't be afraid to make mistakes because they're a part of the learning process but I just can't help it. I cannot control my thoughts at all and they overwhelm me so much. Anyways, recently I started shaking when I go to lessons because I'm very tense and worried, and she keeps asking me if I'm okay and seems really concerned for me. I wish I could just open up to her about my anxiety and tell her that I feel nervous when playing, but I'm afraid of her reaction. She's such a wonderful person but I'm afraid she might not care or she'll think I'm strange. I know I'll feel so much better if I talk about how I've really been feeling, but I don't know how to tell her and it's so hard because I never open up about my anxiety to anyone.