I "binged" private things from my school account?

Anything you do with a school account (or work account) can be seen by the school and the school is legally required to keep that information for a certain period of time. Whether or not your school has anything in place to look at what people are doing on the accounts proactively is another thing, but most don't have the resources and will have basic functionality that flags pornography and such. I don't think you would rise to that level. Most are only going to be reactive in cases other than things like pornography like if someone complained they could go in and search what you were doing.