Hello, well, truthfully, I don't think this sounds like schizophrenia. That one statement is not really indicative of someone living with the kind of paranoia that schizophrenia causes. Schizophrenia is pretty debilitating and would think he'd not be functioning if he had a late teen onset of this. More likely, deeply depressed. It's rough because he is 18 and you are probably worried to death about him. Can you insist he see a psychiatrist? Can you talk about how he felt better on medication? Because I really can't tell you for sure though where he is at with his mental health state, evaluation really is important. While I doubt schizophrenia, only a psychiatrist can rule that out. I'd perhaps ask for family counseling as a first step. Talk about how you want everyone to feel good about each other in the house and you want to know how to be a better parent--- that way he will be more inclined to go. And getting him to go is important even if in the guise of family therapy. He'd be able to then have a professional involved on some level.
Do you fear he is a danger to himself or others? There is involuntary holds they can do also. That is rough because it may cause him to then back away from you but if he is spiraling downward, you would have to do it. Main goal is to keep him safe and you guys safe living with him.
And eventually-- and this is really hard I know, mom to mom, but you may have to instill things he must agree to in order to live with you. Treatment for depression being one of them. Hopefully it doesn't come to that. Keep in touch and let us know how he is doing (and you too). hugs