I do have health anxiety to a point. So what I do is work to prevent illness.
So instead of checking my breasts, I massage them in the bath, and do lymph node drainage with a textured cloth.
I eat well and take supplements.
This way I feel I am preventing illness, and if/when I get sick, or my child get sick, and I panic and the internet says 'yeah, that's probably cancer' I can rationalise to 'no, you eat well, take measures to ensure your and your family's health, it's probably going to self-resolve'
and I have been right so far.
I think it's about attitude. Stress facilitates illness, the body is in a state where it can't fight off disease. So, eradicate the stress and you are more likely to be okay.
I look at it that way; if I am anxious about sickness, why would I increase my chances of becoming ill by stressing over it?
It takes about an hour to get back to normality once I've gone over the whole 'have to go to hospital and be diagnosed with instant death'