Heat rash help please!

My 1 month old has a heat rash on her cheeks, ears, neck and back. Pretty much where my arm rest against her when breastfeeding. It's so hot here and we spend our days in the AC. But after a feed I still peel her off my arms sweating. I called the child hotline for advice and they recommend tepid water bathing each day, which I've been doing, but it's not improving, maybe even travelling down her back a little more. Is there anything else I can do which is safe for newborn skin?