I'm going to start with 'Congratulations' and I mean it. I'm glad for you and most of all the buck, that you were able to harvest the animal and it died in short order.
That was all wrong though. No new bowhunter should take this as an example how bowhunting should be practiced, you straight up got lucky.
There are honestly only two problems. Never take a shot at a deer head on, and never ever take a shot at a deer head on that has pegged you. It's also not wise to take a shot at a deer that has you pegged even if it's broadside. They're quick. Often case scenario is they jump the string and you clean miss. Worst case scenario, and the arrow strikes the deer high or back missing vitals.
It's our responsibility as hunters to make smart choices when the decision is made to drop the hammer. That wasn't one, and I assure you atleast 50% of the time you wound the animal and don't recover it with that shot. If those odds are cool with you then there's a problem.
I'm hoping you know a whitetail anatomy and if you don't you shouldn't be bowhunting in the first place but if you do, then you know the bone you had to thread the arrow through to get to the heart and lungs. The brisket and shoulder blades are tough bones to penetrate. I'm honestly pretty suprised that a deer that was on alert still got hit square with your arrow straight on but again, sometimes it's better to be lucky than good.
Regardless, you got the buck, congrats. The only reason I make this post is I truly hope you give it more thought if put in this same position again - and you will. You might not be as lucky next time and no hunter likes to have a wounded animal on their conscience.
Cheers
jf