People often project what they do onto you. *hugs*
This. Cheaters, or those who would like to cheat, often assume the other party is just as they are. Of course, the Schizophrenia complicates matters, but whether she is cheating or not, this kind of double behavior standard is NOT conducive to a healthy or lasting relationship. I would try to approach the issue with as much compassion as possible, but in the end, only you can decide what you will or will not put up with.