Is their any home remedies to make chapped, red, itchy lips go away?

Bag Balm. Bag balm is an old vermont formulation that was originally made for cow udders. (yes, cow udders - that's the "bag" part.) it comes in a little square green 1-ounce tin; some drug stores carry it, and I think you can get it online. Nothing works better on chapped lips, in my experience. Good for really dry hands and feet, too. (no financial interest.).
Chapstick. Use vaseline or any oily /fat containing substance over lips to keep moisture sealed in. Chapstick will help.