For heat rash I try to keep my baby as cooling as possible. Once I feel that she’s sticky, I wipe down. Change to those mesh singlets instead of her normal cotton onesies. At night if no aircon then I’ll wear short sleeves for her with socks. With aircon then PJ with footies without blanket. Her heat rash cleared within 2 days.
For eczema on face, sebamed protective facial cream works very well on my baby. For body I can’t advise cause she only had eczema on her face.