異位性皮膚炎 Eczema

i never thought my baby would have eczema before since me and my husband don't have it in the family.  My baby's face rash started when he was 2 months old. It was only a little bit on the face, and got worse on cheek, forehead, ears, chin, back, and arms.  his entire face is covered with redness and dryness. i've searched and used many products and none of them seems working.  Doctor also prescribed hydrocortisone 0.5% for the face rash. but after putting it on for weeks, it didn't go worse, but it didn't gets better either. Everybody knows steroid has side-affect, so i wouldn't want to use it for long period of time.  i bath my baby w/ 茶葉水 according to doctor's suggestion. It helps recovering the open wound, but his skin felt more dry afterward. Moisture is the most important part to prevent eczema, but since my baby's face as a lot open wound, we could not put lotion on him as it sting his face. 
Here are the products i've used so far.
1) AD 小護士
Product from Japan. A lot taiwnese moms are talking about it and said it keeps the itchiness down and keep the skin moist.  it's the 1st item we try for my baby's face, and it seems working, so we continued for 3~4 weeks.  but it couldn't hold his eczema down and we discover it actually itches his face.  so we stopped it.
2)  at 3 months, his rash started to grow, so we have to use hydrocortisone. it was on and off, and never completely recover. We also tried to changed our milk to hypoallergenic formula enfamil  nutramigen.  but our baby doesn't like the taste and doesn't sleep well with the new formula.  after 1 week with no improvement, we go back to the old routine. [5/20~5/24]
3)  Avenoo baby
it was recommended by our doctor. It looked good the 1st time we put it on, but my baby's face started to react the next day. his eczema got worse, breakouts and watery.  i tried twice, and each time is the same thing. looked good at the beginning and got worse the next day. i would not recommend it and would not try it again.[5/25~5/26]
4) Cetephil
i researched online and gave it a try.  i brought lotion designed for eczema, and safe to use on baby as young as 3 months. i put it on after bath on his face, arms and legs. it helps soften his skin a little bit, but he still has face rashes. when he scratched his face, the lotion wouldn't work on open wound as it sting his face. [6/1~6/2]
5)  at 4 months, he started to have rashes on eyes and nose. it seems more like milk allergy to me then the outcome such as weather or detergent.  We started trying hypoallergenic formula again with similac alimentum.  also moved on to a new cream Vanicream, recommend by our friend.  will see what happen. [6/3~6/16]