hmm. Okay that's certainly a cause for concern and attention, but perhaps there is a sense of shame about your parenting abilities that then causes the anxiety?
I had some old school religious ideas installed in my head at a young age. Many things but certainly the idea that illness is symptom of sinfulness. someone is sick because they are bad. for me this caused quite a lot of anxiety around my own health but also the health and wellbeing of my children. When they were unwell I interpreted that as evidence of my own sinfulness. I was taking on responsibility for things that I could not actually control out of a sense of shame and that caused massive anxiety.
Now, when I manage to accept appropriate responsibility... responsibility for paying attention and responding to illness, and I don't take on responsibility for the illness having existed in the first place, I experience dramatically less anxiety when myself or others are sick.