Sounds like you might be thinking of the movie Dead Beat (1994)
The movie's based on noted loser Charles Schmid (also the basis of The Lost
). The lead character dresses like Elvis, wearing make-up and cans in his boots to appear taller. He spends the movie lording his "coolness" over some dumb high-schoolers and then ends up killing several girls over the course of the movie.
If it's the right movie, then there is a rich girl who spurns his advances and causes him to go into a rage where he trashes his house. Then later he ends up killing her in the desert (off-screen).
I couldn't find any clips, but here's a picture:
Not a great movie. You can see it on Netflix Instant.