better u bring your baby to clinic.my case also same with u but more worse on scalp area untill become eczema.then the doctor suggest to use virgin coconut oil for the whole body and the scalp area she provide me the cream and antibiotics.she also advise that mother need to avoid seafood,egg and many food.
Just use baby oil for the cradle cap n remove it by using comb slowly.. I think you should bring ur baby to the doctor n ask about ur newborn skin condition.
Jaya comel