I constantly worry about my kids getting harmed or sick. Do I have a neurosis?

Not necessarily. It is common to have concerns over your children, they are after all an extension of you. If you feel anxious or excessively worried, try some natural techniques like 10 deep breaths in through the mouth and out through your nose, listening to the air flow through. In addition, mint or peppermint tea calms you as well as your digestive system. And a number of herbal teas serve this purpose.