Dr House is going to walk in on this thread any minute now.

Lupus?

I'll think of the proper name soon, but it sounds like what are commonly referred to as school sores here. Very contagious and they seem to appear from nowhere. If there have been other school aged or daycare kids around, it would be very possible for the little one to have picked it up.

I think the doctor would be a good place to go.

Impetigo. That's the proper name.