School admin sees what I am doing on the computer. How can I stop it?

[Richard]

Please help.
On the last day of school about a week ago, I got a free period on computers due to it being the last day. I took this opportunity to play Counter Strike at school. I soon got a message from the school admin saying that it was banned. I happily got off the game as there shooting and stuff, so I went on Mario. I was then remotely logged off by the admin. I got in trouble from my teacher, who was telling me to stop going on the computer because he was scared that he'd get a bad reputation. Mario is not violent at all, so I was confused. I immediately logged back on and went 9gag, having fun looking at funny posts with my friends, until the school admin sent me a message saying 'This is not appropriate for class time'. I got really mad as we had free time, yet the admin didn't know and kept warning me. My teacher got angry with me again, and said that we'd never have a free period ever again, thanks to me. I was super mad then, because the admin kept warning me and logging me off while everybody else in the class was playing games like Sonic and Meatboy. I want to find a way to stop the admin from seeing what I am doing. Please help!!!
@Gardner
As I mentioned we had a free period, so we were allowed to do whatever we want. I don't want to sit there for a full hour watching others playing games without getting ratted out while I'm getting caught every 5 minutes. Btw, as a lower year level, I only get 1 free period a term (last period of last day of term)
@James
Thank you for your help. Might want to wait for other answers though.
@t12_incomplete
It is the schools computer and internet. I'm just wondering if there is a way though. As I mentioned it was a free period so I wanted to do something fun. Our own teacher even gave us permission to play the games.