Schizophrenia isn’t DID (dissociative identity disorder, previously known as multiple personality disorder), and truly has nothing to do with it. I’m pretty sure the public misconception dates back to when we didn’t really care what was wrong with someone’s mind, but rather only that there was something wrong with their mind, so DID would be lumped under schizophrenia. Schizophrenia itself has a lot more to do with intense paranoia, hallucinations, etc., and many people will say that if you think you have it, you don’t.
You may still want to get checked in case you have DID or hypochondriasis (a sort of obsession/paranoia dealing with diseases, mental or otherwise, and an overpowering belief that one has these diseases), but that would more likely be to put your mind at ease than anything.
Also, dream interpretation is an almost entirely discredited theory. Nowadays Freud is credited with little more than getting the ball rolling for the study of psychology, so be careful what you take from his theories. It’s actually fairly close to being proven that dreams are simply the product of random neural impulses affecting the brain because the perception areas of the brain remain active although the sensation areas have been turned off, or something like that.
I actually talk to myself all the time (audibly or inaudibly) as though I were talking to another person and am somewhat paranoid myself, in that paranoid thinking is often the norm for me and I have to actively convince myself otherwise. I also often have negative thoughts, and, despite usually not being depressed/emo/etc., the first words that come to mind when I think of a random word lately are “death” and similar words. However, from my own perception I’m able to control this fine and haven’t had anything I could call a full-blown hallucination, so along with this and the advice of my family and friends I attribute this idea that I might be schizophrenic to hypochondriasis. In my book, depending on how mild you have it if you do, it may be better to not know/ignore the fact that you have it rather than giving in to a defeatist personality or blaming your problems on it. Of course, if it’s a serious enough condition, you definitely would want to get help for it.
Above all keep in mind that one of the five indispensable definitions of a psychological disease is that it keeps one from effective/normal functioning. If your abnormality isn’t showing any real bearing on your life, it may be better to just ignore it.