Well, you are already doing what you can...I was going to say that you should make an appointment with a therapist trained in treating this kind of anxiety. Some people are just more "worry-worts" than others, some people are more laid-back, and different people worry about different things. The thing is, worrying about every little thing, and automatically thinking the worst rarely does any one any good. It's one thing to blow off something that could be significant, or ignore the obvious, but getting worked up about every little possibility is not productive.
I think one of the things to realize is what is the probability of something being more serious than it is - usually it's pretty small. Yes, a stomach ache in a 5 year old could be cancer, but really, what are the odds? Doesn't every kid in the world have to deal with colds and an upset stomach once in a while, and doesn't it end up being nothing more than that? Again, I think you need to put things in perspective, but you may need to see a professional to do that.
Does all this stem from your parents or your childhood in some way? Have you ever considered that your obsessive worrying could in some way affect your children and get passed on to them? I'm not saying that to give you one more thing to worry about it, but to help you to see that there is a point where worrying becomes destructive instead of productive. And you need to start asking yourself if your being worried about something is doing one or the other.