A.H.
Sounds like you're already thinking about laundry and allergy issues. Try a different sunscreen or leaving sunscreen off for a while too (hard in summer, I know). We use "Conntry Save" laundry detergent. It is really mild and rinses thoroughly. Also economical.
My children both have on-and-off eczema and allergies. I do usually bathe them daily for the routine, but I almost always use Aveeno Colloidal Oatmeal in the bath. Money-saving tip: don't buy the packets sold in the baby section. You're buying the same thing for more money. Look for generic brands (CVS has a good one) and add 1/3 of a packet to a shallow warm bath. And you can skip soap every other day.