Umm here goes a couple of songs that might be good to analyse,
Alkaline Trio > Another Innocent Girl
It's not written in the first person but is about the speaker, there is quiet a bit of ambiguity you can go into.
Alkaline Trio > Maybe I'll Catch Fire
definately a lot of thoughts and feelings here but might be a bit blunt for analysis.
Jenny Was A Friend of Mine - the Killers
This has a similar theme and narrative to the 17th centuary peom "Porphyria's Lover" by Robert Browning.
Fast Car > Tracy Chapman
Lovely song, definately worth a look, it is about escaping
Manic Street Preachers
Any of their songs has tons you can analyse, here are a couple of relevent ones
Black Dog On my Shoulder- about depression the 'black dog' as Winston Churchill called it
Faster- only try this if you are feeling ambitious, it is very poem like, it is basically the distilled thoughts and feelings of a very desperate man.
My Little Empire
Try this site to get you started if you don't like the above suggestions
SongMeanings