E.B.
I definitely recommend seeing a dermatologist, but in the meantime, speak to the pharmacist who filled the prescription for Permethrin. The pharmacist will know the exact strength and manufacturer of the Permethrin, and will have information about long-term side effects (if any). The pharmacist can also speak with the manufacturer's medical representative directly. Pharmaceutical manufacturers keep track of side effects, and perhaps they have seen something similar. At the very least, the pharmacist may be able to suggest an over-the counter cream to relieve your symptoms.
Be sure to keep a record of the shampoos you use currently, any skin lotions or creams you are using (and your kids too), any over-the-counter creams you've tried.