Affiliate Marketing Secrets

So here is the story: I logged onto a school website (on my home laptop – no way affiliated with the school) so that I could check what my schedule would be for next year. Unknowingly, I somehow activated my schools web-filtering software on my computer. I closed the tab (and I think the whole browser) when I was done. I then entered into Private Browsing and searched some… adult oriented material. I got a Fortiguard web filtering page that said that the page was blocked due to adult content. i then cleared my computers Temporary Internet Files and cache and stuff using CCleaner and tried again. This time i could go anywhere on the web…
Due to an overwhelming sense of curiosity, I tried it again and got blocked again. I was only after doing researh on Fortiguard that I found out it logs my query and the IP address.
Anyway, my question is: As this apparently gets logged along with the IP address… does my school have any right to get me in trouble for this? Like could I get in trouble, or anything?
It is middle of the summer, on a private computer (my parents bought it, the school has nothing to do with it), off school premises and without my knowledge…
Also, do they have a right to activate the web-filtering without my knowledge or consent? No where on the site does it say that this occurs…