I guess we don't really know what Cheater is because it is a made up role, but it did come up green, so I have to assume town-alligned, and for that I have to believe her that there is a Psychologist. However I do not believe you are it and I suspect she was trying to get you killed for voting her out. The fact that you weren't could indicate you are in fact a killer. Then again, I don't know why mafia would want to kill the Psychologist since their power isn't useful against mafia.