It’s very unlikely that this incident will impact your chances of admission anywhere. But for what it’s worth, your explanation could use some work. How did your teacher find “a piece of paper with study materials” that you “accidentally left in your sweatshirt?” Did your teacher search through your sweatshirt? Or did she perhaps notice you removing the piece of paper during the test?
I ask these questions because there’s only one way this could hurt you—if you seem dishonest or evasive in your explanation of what happened. Honestly, you’d be be better off saying: “I got caught cheating in high school, was disciplined by my school, and I haven’t done it again.”
Seems this is a non issue, actually-- was skimming the threads when I came across someone who’d asked H and N what they mean by “any educational institution” and both had replied post-secondary and up. Going to email to see for myself, but nice to know.