Pla... that's not how guns work.
Also, while any bullet can kill you provided it hits a vital area, a .22LR round will not cause more internal damage than a 5.56 NATO round. If the bullet stays in you (without hitting a vital), that's actually a good thing. People who are shot often have the bullets left inside them because it's safer to do that than remove them and potentially cause further damage. Meanwhile, exit wounds will cause heavy bleeding and will potentially be fatal.
And regarding body armor, there's no such thing as armor that can simply shrug off bullets. If you get shot, it's going to feel like you got punched in the gut (or worse), no matter what kind of ammunition is being used. That's if you're lucky enough to not have the bullet just straight up pierce the armor, even.