There are two things I say to myself that help me when I'm having obsessive thoughts and my brain is trying to sabotage my happiness. The first thing I tell myself is it doesn't matter if you stand on your head, twirl flaming batons with your big toes, walk a certain way, avoid certain cracks in sidewalks, or in our case, think about things until the point where you have no more mental energy left. Bottom line is, things are going to happen regardless of how much you do and think to prevent them from happening. Just like time, life doesn't stop and things are going to happen.
The other thing I tell myself is that I don't want to look back on my life and think about all the thousands, millions of hours I spent being obsessive about things or being anxious about things. OCD has a way of robbing us of our happiness. Now most might disagree with this, but OCD is trying to do the right thing for us, but in the wrong way. In regards to that, our OCD keeps us in check, keeps us responsible, keeps us on our toes, lets us know that there is something really bothering us that needs our attention, so forth and so on. The only problem is that it goes to such an extreme level that OCD sort of "over" does it whereas a simple, "hey I'm worried," would work just as well.
Alot of OCD is about control. If I had to guess, I would say that the underlying issue with you and your child is the fact that you want to be a good parent and keep your child healthy, happy and safe. There are some things, however, that we cannot control like illnesses, and accidents. Thinking about these things is enough to drive a parent up a wall because we only want what is best for our children.
Just like I said before, life happens and we have to be ready, but not to the point where we constantly think about it. I do the same thing. Sometimes when I'm out riding my 4-wheeler I get a sense of adventure and do something I wouldn't normally do. Then I think about it and say to msyelf, "gosh that was stupid I could have really been hurt." Problem is my OCD takes it to another level and says, "OH MY GOSH!! I can't belive you did that!! That was SO STUPID!" Again, my OCD has gone overboard trying to protect me from doing stupid things. Fact of the matter is life happens and it's full of risks.
Hope this helps!!