Milan, what you are seeing and doing is very often experienced by archers, bowhunters. You need to slow down and pick a spot. You know this from target shooting. But we all get excited. Folks that never hunted have no clue.
There is a physiological response we have when we are ready to take a critter's life and we actually have a weapon in hand. A camera won't do this. Not actually wanting to kill something, even with a bow in hand, will also not produce this. It is likely related to fight or flight responses.
One of the unfortunate responses is acting on "auto pilot", forgetting much of your mantra and rules of shooting. This is why it is so important to do a couple things. First, ingrain the shot sequence so there is no need for thought, you always do (this).
Second, practice seeing critters up close. Go hunting, go hiking, go to a museum. Every time you see a critter, be it a dog, a cat, a deer, an elephant, go thru a sequence. Assess if it is a shooter and then pick a spot(even though it isn't).
Tell yourself where to aim, and why, then focus on it. Wait for a broadside or slightly quartering away posture, Wait for the animal to exhibit signs of being at ease, not stiff and ready to dodge the arrow. Wait for the leg to move forward. Then say "bam !" or whatever you want to say to represent a release.
Do this all the time and it gets a bit easier to do when the time comes. Then, go out as often as you can and shoot some. That practice is needed as well.
Good luck and try to be less aggressive. Enjoy yourself and what you are doing. That is a big part of the game as well as a kill, maybe even bigger.
ChuckC