Not being a doctor, of course, I can't diagnose you, but I'd say that what you're describing sounds very much like OCD. It's not surprising that the doctor would have diagnosed you with GAD, since anxiety disorders tend to overlap with each other (I think most of us OCDers have other types of anxiety - GAD, social anxiety, health anxiety, etc., also).
One of the very worst things about OCD is the intrusive thoughts - the things that you fear the most start appearing before your very eyes. I've had many harmful thoughts involving myself or people around me - they don't reflect my desires at all
, which is why they disturb me so much. Personally, my OCD always made me feel so alone. My constant thought was, "Nobody else has these thoughts. Why do I have these thoughts? I must be crazy. I must be some brand of insane they haven't even defined yet." But in truth, we don't know what's going on in other people's heads. I think everyone, even the most "normal" people we know, has these thoughts pop into their head, unbidden, from time to time. The main difference between that person and a person who's got OCD is that we obsess over it. Because we're afflicted with anxiety, our natural reaction is to worry over these things, over and over, and assign a significance to them that they don't really have.
It's so much easier said than done, but the best thing you can do for yourself when you have this kind of thought is to recognize it for what it is. Tell yourself that as frightening as a thought is, it's only a thought, a product of your anxiety, and it has no power over you. Then just file it away and focus your thoughts on something else. This is not a simple process, and like most anything else, you'll have to do it over and over again before you really get the hang of it. Many folks here swear by CBT, and it's one of those things that I've really been meaning to get myself into some one of these days soon. If you can, find a therapist. One who specializes in OCD and anxiety disorders would be especially helpful. In the meantime, you'll definitely find a good support network here.