What should you do if your baby has eczema all over his face? As the temperature continues to rise and the humidity becomes higher and higher, more parents find that their children have eczema. Eczema is a very common skin condition, but it can be very dangerous for babies. Babies have very delicate skin, and a flare-up of eczema can be very painful for them. So, what should we do when a baby has eczema all over his face?