This is implied in the show, even if it's not official. She a harbinger of disaster, she wails when she tries to sing, and she's doesn't look entirely human. Also, you only ever see her female relatives (It's a well known fact that banshees are always female), and they are all remarkably similar to her. This is bacause banshee genetics are different. Banshees procreate by mating with males of other hominid species - Often humans, but also fairies, elves, or even vampires - but their offspring will always be daughters, and always banshees.