Maybe some type of fungus? Look up on line about Apple Cider Vinegar and fungus as I am pretty sure that would help, by rinsing the dog with ACV and water mixture daily that might kill off the fungus. Or maybe Tea Tree Oil? That is also a fungicide but it is stronger and might not be good for them if they lick it.

Sounds like it is something caused by all the rain and water from the storms, and fungus is the first thing that comes to mind. There are also medicated shampoos for fungus too.