L.S.
YES! My son had the same thing, along with a possibility to develop asthma (the two are related). My pediatrician put him on amino fatty acid supplememnnts (she recommended Carleson's Lemon flavored cod liver oil, 1/2 tsp a day -- and he loves it)
In addition to that, she recommended aquafore -- but I, too, did not want petroleum by-product on my baby, so I got the non-petroleum equivalent at wholefoods : "No petroleum jelly" All he needs is a moisture barrier. My pediatrician instructed us to apply it to his damp skin to lock the moisture in.
It worked!
Good luck!
Lots of Love,
Linda