Everyone has some amount of paranoia. Especially when anxious. You describe a little more than that though. Do you have hallucinations about the things you are paranoid about? Do you hear voices? Have paranoid delusions? Almost everyone with paranoid schizophrenia has auditory hallucinations and believe they are being persecuted or there is a conspiracy against them. Do you alter your life due to these delusions? That is a distinction a psychiatrist can make for you if you explain what is happening. So, perhaps you suffer anxiety as a disorder and paranoia as a disorder but not to the extent of paranoid schizophrenia? Paranoia and anxiety are similar in that they represent fear. Zoloft will work for anxiety, calming the fear. Anxiety can make you feel paranoid. That's for sure. However, when you start talking about the FBI following you and such, you should dig deeper in making sure a further diagnosis isn't necessary so you can be properly treated. How long have you been on Zoloft?
If you went to your regular doc, he can't actually diagnose you as he isn't an expert on mental illness. To get a diagnosis you'd have to see a psychologist or psychiatrist. Also, at least when I started out on this mad journey, doctors never put you on meds before trying talk therapy of some sort first. I'm amazed at how many people come on here that have been put on medication as a first resort. There's no way for anyone to tell, including you, if something more than anxiety or depression is going on without talking to you for awhile. You also don't say how much this is affecting your life, and we have no idea if something happened in your life to trigger this fear. That's what psychologists do -- they talk to you enough to figure this out. Regular docs don't do this, aren't trained to do this, and aren't well trained in the meds available (well, some are, as some regular docs did their residency in psychiatry before deciding not to become psychiatrists after all, but psychiatrist aren't that thoroughly trained in this stuff, either -- their main training is in the medication used when it's necessary to use it, though many of them will go for continuing education by psychologists to better prepare them). Without a proper diagnosis, choosing the proper medication, and whether you need medication or not, isn't really that easy to do. Given you seem to be fine in every other way, it doesn't appear you're at the place where medication is necessary yet, but even if it was, you're right to question whether Zoloft is the right med. I have no idea personally, but you don't sound like you're suffering from chronic anxiety or depression, you sound like you've developed an obsession with this one thing.