Bill, my most sincere condolences
Many years ago, Boomer...the cocker spaniel that was with me before Einstein...contacted lymphoma. After almost a year on doggie chemo, his quality of life was gone...his breathing was labored...he was lethargic. I kept questioning my decision to end his pain as I drove him to the vet. But, when the vet administered the shot of diazepam...as I gently stroked Boomer's head and spoke to him...Boomer looked directly into my eyes...and reached up slightly to lick the end of my nose...before his head fell softly into my hands. I like to think that final momentary gaze into my eyes and the little nose lick was his way of thanking me for a good life and for ending his suffering.
Damn, I still get misty when I recall those final moments. I do feel your pain bro...the pain never really goes away, but you do learn to live with it.
You absolutely did the right thing for that deer. Ending the poor creature's suffering was the only humane thing to do.