So she never realized her power when she was a kid??

She didn't have those abilities up until after she died and pulled the "Jesus"

It wasn't that clear, but maybe it's something that manifest itself around puberty. And as a kid, she probably had superficial wounds that all kids get. No one pays attention to how fast their wounds heal, unless it was one of a serious nature.

She only became the immortal creature at that moment. For whatever reason she was the one chosen to replace Andy.