C.O.
It's not about dirt - dirt is GOOD for kids - they NEED IT!!! Don't hide your kids from things - dirt and other people help build your child's immunity. I know that's not the POLITICALLY CORRECT thing to do - but I'm not a PC person.
If they are white - it's musceloum - it's a "virus" (NO DO NOT PANIC) that kids get. If they are just red - it's most likely excyema (spelling). You can try and figure out what is causing it by changing your soap (laundry and body) ONE AT A TIME for at least 2 weeks - if you use Tide -that would be the first thing I drop. Try the Purex or All "free" items.
Diet has a lot to do with it as well - so if the topical items don't make a change - SLOWLY try diet.
In the mean time - see the pediatrician - set your nerves at ease.