Eczema is not contagious. I've struggled with it on my hands for years. I use cetaphil lotion sold at Walmart. Doesn't burn and it isn't super greasy like other brands. The only time I wouldn't handle baby is if you're scratching so much that you have open sores. At that point it's probably time to see the doctor anyways. Just DONT scratch. It'll make it worse. If you feel itchy I blow on it and the itching subsides. Hope this helps!