These are phrasal verbs. You can study whole lists of them if you google them, but here are the answers:
1. get carried away: means you enter of face of unconsciously doing something. For example, "the TV show was so interesting; I got carried away by the story". So in your example, I guess the speaker gets carried away by thinking about that person.
2. turn it up: a physical action to increase the magnitude of something, in most cases the volume of a sound source like a radio. "I can't hear what the TV host is saying. Can you turn it up?"
I think the example you gave is from a song. So maybe she is saying "turn it up" to drown out thoughts of another thing.