I saw two three legged deer this year archery hunting. I have seen the doe for three years and the buck for two years. Both were healed over and the deer appeared to be doing well with good body shape. What we think is a fatal wound may not always be. I feel you dilemma though. Even though we hunt, which involves killing, we don't want any animal to die a lingering death.
If a deer comes by with its guts hanging out or lower jaw blown off, sometimes it may be best to do what needs to be done, even though it may not be legal.
In the situation you described, I think you made the right call at the time. Hopefully you feel better just from hearing from others here.
I support all hunters, regardless of weapon or technique!