There's 2 songs that I like in 10 things I hate about you.
The first one is played every time the character joey is in his car. I believe it is a rap song.
And the other song starts kind of slow then gets faster. It goes "outside all around me makes me happy like I do." or something like that.
Do you know the name of these songs an or singer/band

I wish I knew all the songs, artists, and lyrics from the movie, But I don't. But I did find the soundtrack for the movie, so hopfully you can find the songs that you are looking for.

10 Things I Hate About You Soundtrack, 10 Things I Hate About You Lyrics >>

The second one you're talking about is sunshine on my window by letters to cleo