Did Petey actually kill himself or did someone else kill him?

I think its heavily implied that he was indeed that big an eejit. He makes a statement prior about how he's handy with the steal, or words to that effect.
I thought it was a brilliant bit of dark humour. Unexpected and well timed. Very funny.
Getting back to your question though, yes, I believe its intended that he did accidentally shoot himself and no other party was involved. Lets be honest, we all know at least 1 gobshite like that ;-)