My daughter has a red mark that hurts from an ice pack. this wa 2 days ago. there are no blisters, but it's warm. will this heal on its own?

Yes it should heal: If there are no blisters, it should heal on it's own in a few days. If the area continues to get more red, warm, and hard to the touch, it is possible that she is developing a cellulitis (skin infection). if it's getting worse rather than better in the next few days I would have a doctor look at it.

Frostbite: What you describe sounds like the equivalent of a sunburn, caused by a shallow form of frostbite.It should heal within a week or so. Just keep the area clean and look at the site daily.