For the stage fright thing you might try this old public speaking aid. Temporarily imagine everyone in the room, except you, is in the nude! Also tell yourself you know for a fact that their combined incomes is only a tenth of yours and that they all have bad breath. Under these conditions why would you really care what they thought about anything!?? The pressure is removed!!
Attitude can be a good thing!
On the shooting part, a great old trick is to have a friend load your weapon with only one round -- or not. They do it with your back turned so when you squeeze the trigger it might go bang or just click, you don't know whats gonna happen! Focus on just the weapon, see what happens when it only clicks, repeat this a few times every range trip. You might notice some very bad habits that require attention, when you are not distracted by the muzzle blast and recoil.
Like people said, practice makes you better. Its kinda like backing up a car trailer, if you have to think about it, that ain't good. Eventually it all becomes second nature and you'll even impress yourself like you did with the rifle.
PS - Welcome to the forum! Ken