Cradle cap and dry skin

My Lo. (5 weeks) has very dry skin. I moisturize him after his bathes which are every other night. And wash comb through and messege message his scalp during his bath time also. Plus I let olive oil sit on his scalp and then comb it on alternate bath nights!! Can someone please tell me what I'm doing wrong or what can help his skin!! I can't take his dry skin and breaking out anymore!