You know you should sit down and talk to them problem shared is a problem solved I'm sure they would respect you for that
Take a deep breath ...nobody is perfect if that doesn't help have a kit kat
Everyone makes mistakes. Learn from the experience and move on.
you've told your parents and the teacher. have you told the person you falsely accused? (love your screen name! WHEN you achieve it, you'll be a happier, more confident person.)
assuming the teacher didn't confront the student, you got off very lucky. if the teacher did, what do you think you should do? nevertheless, please chalk it up as a very necessary lesson in life not to use conjectured "evidence" to accuse anyone of wrongdoing. as you have experienced, our mistakes could jeopardize the well-being of another. the fact you feel horrible about it speaks volumes to your capacity for caring...and clues us to your developing character. just don't be so quick to judge others' guilt without seeing irrefutable evidence for yourself. you're alright in my book.
Youngling, why did you remove all the details from your question? People won't know the context of your question. Anyway: guilt + genuine remorse = courage to confess.
own up to it and apologize....people make mistakes...you'll be a bigger person for it!