I finally remembered the name of this game! I've been trying to remember for years, and all of a sudden it just came to me yesterday. When I was a kid I used to go to my neighbor's house and play this old DOS game, and after all these years it's still fun. If you've ever played any of those "escape from the room" games on the internet it's kind of like that, except a full game. You're a kid who collects things in his backpack and use them to get out of certain situations as the story progresses. You have a trouble meter, and the more of a little nuisance you are the higher the meter goes until you get shipped off to military school.
You can download it at this page. You will probably need something like DosBox to run it, which you can get from dosbox.com.