OP, I posted here once about a similar issue and got jumped on, but I'll repeat it briefly for your benefit.
I used to babysit for a particular family that eschews modern medicine (everything from vaccinations to antibiotics), hand washes all their dishes in lukewarm water with the mildest soap I've ever seen, and is perpetually sick. REALLY sick! Months-long infections, coughs, congestion. Every time I'd work for them I'd get sick, too! It was terrible. Eventually I had to stop because I wasn't getting sick anywhere else and don't you know, I've made it all season without a single cold this year. I have gone back once and made a point not to eat anything and to wash my hands every ten minutes and I made it out safely, but that's not practical for a FT nanny job.
You may, unfortunately, need to work for somebody else. You can always sit down and try to negotiate more sick days by pointing out there have been more illnesses in their home this winter than average, but that's not guaranteed. Good luck whatever you do! Stay well
