Young boy kills his family, at one point he's stabing his arm with a tac in class, likes an older girl but finds out she has a boyfriend so he kills her cat and plants it under the boyfriends car.

I considered "Mikey" (1992) starring Brian Bonsall. However, the synopsis refers only to him murdering his family. It doesn't mention killing a cat. / I did find a mention of "self-mutilation".

http://en.wikipedia.org/wiki/Mikey_(film)

I also checked out "The Paperboy" aka "The Paper Boy", which is from the same time, but I didn't find any similarities.
http://en.wikipedia.org/wiki/The_Paperboy_(1994_film)