In CSGO, they have something called 'aim punch' which flicks your aim up when you get shot and happens more if you don't have armor, compared to when you do.
They also have a 'slowdown' effect when you get shot. I don't think it's accurate to say that you can't 'turn sideways', it should only affect movement.
I'm also a little confused on what you mean by 'we should have the ability to move to kill the enemy first if we manage to hit a bullet in the head for example'. The game supports both fast and slow pace playstyle, and it rewards you for choosing the correct one to utilize, while of course aim being the finally variable in whether you win a gunfight or not.