THE UNIVERSE AGAINST HER - Telzey Amberdon Book (1) One (by the author of The Witches of Karres)

Telzey Amberdon, at age 15, had enormously developed psionic powers. She could read, as well as change, human minds! In part I, she enjoys an extraordinary telepathic rapport with a feline non-human. Then her dreams become nightmares dominated by a weird "psionic traffic cop," and she realizes that further exercise of her powers could lead to trouble. Somehow, the interstellar government had found out about her, and had planted that "cop" in her mind to destroy her.