Well, hearing voices in your head is just one among many symptoms of schizophrenia. If you have the constant feeling of confused thinking, false beliefs, depression, anxiety and unable to sometimes accept reality, then your psychologist might be right. But it doesn't mean it's necessarily so, some other health related issue are closely associated with these same symptoms, as those of schizophrenia.
Going back to your description, you made a comment about people close to you who intend on harming you. Have you had such experience before? Has any of your suspicions come to pass? Why do you think people are out to harm you?
I don't want to sound like your psychologist, but the answers to the questions above might be the defining moment of your sanity or health state. And it's probably the reason why your psychologist thinks you have it.