Well, these may not be intended as self injury songs, but as an ex-self harmer [fingers crossed it stays that way] and total music lover, I can identify.

Bad Before Good - Day One
Paper Bag - Fiona Apple
Bleed Like Me - Garbage
Queen of Pain - Alkaline Trio
Razorblade - Blue October
Magician's Assistant - Scroobius Pip
If you can't leave it be, might as well make it bleed - Dashboard Confessional
Little House - The Fray
When I am Queen - Jack Off Jill
A few small bruises - Maria Mena

There are quite a few sites with collections of lyrics, found via Google.