There's good and bads about hunting my friend! You did everything you could do by the sound's of it, thats all anyone could ask for. Alot of people wouldn't of put the time in you did by looking for your deer a few days after, i commend you for that! It's always tough on a person when they don't recover there animal, but thats why it's called hunting and not getting! By the sounds of it your deer should still be alive as long as no infection sets in but these deer are tough critters so i think he will be fine! By most meens if you would of even caught the top of the lung he should of been laying there where you looked. Keep hunting buddy and try letting go what happened! Good luck!!