Maz Kanata says: “to reach her son will take all the strength she has left”. So it’s clear Leia wasn’t coming out of it alive. Rey didn’t kill her.
She feels ashamed that in her rage she didn’t hesitate to kill Kylo, while Leia was still trying to bring back Ben. She’s reminded she tried to bring him back herself, which is why she tells him “I did want to take your hand, Ben’s hand”. Rey feels she’s lost control which is why she goes on exile.