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Bed bugs can cause what you are describing and they can invade the cleanest of homes.  It would require you stripping the beds, washing everything in hot water - probably twice - and getting the mattresses checked for these tiny creatures.  You could seal the matresses in plastic which ultimately kills the bugs;  there is an huge onslaught of these creatures in homes and hotels across the nation.  People even bring them home in their suitcases unknowingly, after staying in hotels infested - and again it can happen even at ritzy hotels.  The bumps fit the profile - not sure about the blisters.  Did they run a fever before it happened - certain viruses also present this way.   Could it be a contact dermatitis or new allergy (though with both kids getting it at the same time??) but I would see if you changed any home cleaning products, bathing, clothing - bed clothes - towels - materials, clothing that they might be reacting to - also any food products that are new that they both ate.   I'd consider using Cetaphil which is very gentle right now for bathing them.  Hope some of those suggestions help - and I can only imagine your frustration with having to wait to see the second doctor. Good Luck!!