Bless you for opening your heart to that unfortunate chick. Unfortunately skull deformities like that only worsen as chicks grow, if she cannot eat at just a few days old, she will absolutely not be able to eat when she's older.
Chickens do hide the fact that they are suffering, so I'd watch her closely for the next week or so. If she seems to improve under your care, you can keep fighting for her. But if she remains thin and does not gain the ability to eat on her own, you're not doing her any favors keeping her alive
Chicks require constant food intake to grow and thrive. Unless you have absolutely nothing else in life to do, you can't meet her needs.
A friend of mine has had to cull her chickens and chicks in the past. She says that the most peaceful way to do it is to hold their faces up near the exhaust pipe of a car while it's running. They just fall asleep in a gentle drift.
Chickens do hide the fact that they are suffering, so I'd watch her closely for the next week or so. If she seems to improve under your care, you can keep fighting for her. But if she remains thin and does not gain the ability to eat on her own, you're not doing her any favors keeping her alive

A friend of mine has had to cull her chickens and chicks in the past. She says that the most peaceful way to do it is to hold their faces up near the exhaust pipe of a car while it's running. They just fall asleep in a gentle drift.