I'm really sorry you and your young hen are experiencing this. If you are willing to make her a house chicken (except for during future balmy warm weather when she will enjoy being outside in the sunshine), & her attitude and spirit remain good, there is no need to euthanize her.
It isn't that her frostbite is currently "getting worse", but that her feet are Visually dying. The damage is done, and there is nothing you can do to reverse the process. Mostly all you can do now is wait for the dead feet to detach from the live tissue. Auto-amputation is an internal healing process that could take weeks or months; each case is different. Keep her warm and keep both feet clean and dry. Her feet will remain painful until the frostbitten tissue becomes completely necrotic and dies. Make sure her appetite stays good. It's ok to offer her some enticing treats such as scrambled eggs or meaworms if that is all she will eat.
I have a hen that lost both her feet to frostbite in February 2021. She now lives inside my house at night (since she can't roost) and also remains inside during cold and inclement weather. But she spends most days outside with her flock, & she even resumed laying eggs this past summer. Your young hen's frostbite is tragic and life-changing, and she will be handicapped for the rest of her life. But if you are willing to tend to her special needs, there's no reason that her life can't still be good and worth living.
Photo taken September 2021 of my feetless hen (Matilda) looking and acting like a perfectly normal chicken except for her wrapped and padded stumps.
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