Don't worry … your bad judgment in 6th grade will have no impact whatsoever on your college process. Applications do ask if you've ever been suspended or expelled BUT …
1. The question only covers grades 9 through 12, so 6th grade infractions don't count at all
2. A lunch detention isn't a suspension or an expulsion anyway and thus wouldn't have to be acknowledged on an application, even if it did occur during high school
So you're off the hook. But, even so, it's wise that you realize your mistake, and it looks like this continues to weigh on your conscience. So let me tell you the story of “Roberta," an old friend of mine. She was awful to her 8th-grade shop teacher. Roberta and a couple of other classmates made his life miserable. Many years later, as an adult, she reflected on how rude she'd been to that teacher and she wrote him a letter of apology. Shortly thereafter, he died and, when Roberta heard the news, she was glad that she'd taken the time to write to him when she did. She still felt bad about the way she'd treated her teacher, but at least she was grateful that she'd tried to make amends.
Although it sounds like your misjudgment was just a one-time deal and not an entire year of teacher-torture, you may want to send your music teacher a card or note to tell her that you regret what you did. I'm sure she'd appreciate this. In fact, if want to go all out–you can even write her a song … or a symphony. 😉
But, meanwhile, you can sleep at night knowing that this one error won't haunt you in the future. You may even have a stronger high school career because you learned an important lesson early.