Sounds like psoriasis to me. my son and husband have it. its inharited andnyou can use steriod cream for it for the babies if doc gives it. i personally havent taken my son for it yet as mybhusband is gone foe time being and since he has it id like him to be there. i have found lotions after bath helps a lot
My son got that bad a while back and it turned out he has really sensitive skin. So we use a high strength hydrocortisone cream, aveeno lotion and pure soaps/shampoos like dove. And it gets worse in the winter with the dry air and all. You could always try that stuff.