Had an experience similar a few years back. There was a dear hit by a car on the side of the road and its leg was hanging by just the skin. Poor thing was trying to run away but could not get out of the ditch on the side of the road. So, I drove by, turned around and went home to pick up my .45 Kimber. Got back and put about three rounds through the heart lung area not more than 4 feet from it. This was before I new where to shoot. Thing was still suffering. So, I aimed for the back of the skull and Finlay was able to put the poor thing to rest. Next thing I know a police officer is pulling up behind me as I'm putting my gun away, so I unload it in front of him, keep it locked open and put it away. He comes out of the car and says "Thank god there are some responsible people in the world! Saved me a ton of paper work."
I was still a bit shook up since that was the first time I ever killed an animal. Even asked me if I wanted to the deer for the meat. Dang, it I should have popped it in the pickup and took it home! Didn't know what to do with it so I left it. For the Coyotes! Ce' la vie!
But don't you dare feel bad about what you did. One thing I was taught even before this happened by my grandfather is "You don't leave a wounded animal to suffer in the woods or anywhere!" Its a merciful thing you did!
Tiller