I'm worried for something I did over the schools Wi-Fi

So I was in class playing a game called Kahoot where you enter the pin the teacher puts up and you enter it you then put a name. Your supposed to use your real name so I put my name. Then opened another tab and logged in using this name. Shrek is (teachers name). She got mad and said she will get people to check who did it. Will they know that I typed that in. I have an account and use the schools Wi-Fi. But the website is https. After that I cleared history and browsing data and logged out from the schools Wi-Fi. It was on an iPhone. Should I be worried

Added (1). Account for the schools Wi-Fi

If the school has the right software installed that lets them track All logins then yes, they can narrow down the source device rather quickly.

Yes, you should be worried.
You can be traced…
Your guilt be will be clear to see.