For the scalp do try olive oil! Preferably non fraganced, i think polyclinics sell at the pharmacy in glass bottles by ICM. Usually apply after evening bath to slough off the dead skin and keep scalp moisturised. It feels gunky to me so i usually bathe off baby scalp during morning bath and reapply again. If things are bad after moisturising skin for months all, i actually went to peads to check if steroid cream is needed. Sadly baby was prescribed because i personally dont like to use on a baby but thats my thinking/preference. Usually start off with a low strength like desowen(brand) lotion. Another option dr will share is protopic(brand) much more expensive but non steroid based. However it does cause some stinging sensation in some people. So let your peads diagnose first if its eczema or fungal or just milk rase or even baby acne then proceed to treatment. I tend to vacuum the house more plus air purifier to reduce dust in the environment too. And eczema seems to flare more in heaty conditions so cool rooms help and onesies only but too much aircon might also cause phlegmy baby. Idk man im trying to figure out too. good luck there
my youngest son used to have bad eczema on face too.. now he don't.. check on food or formula intake too...both u and ur baby... anything that has yeast, please avoid for a week and see if there's any difference...
in Singapore weather, could be too hot. baby should wear one piece lesser than adults. so if adult is wearing 1 shirt, then baby to be shirtless. too hot weather will need on aircon, 21 -22 c
hopefully agape nature works for ur baby