Welcome to BYC!
This is definitely a strange one. Cocci can cause them to go off their feed and not drink either. But you say the droppings are normal and she is not fluffed up. But eyes are closed while standing. Could be a case of coccidiosis, to which you would need to add Corid to the water for 5 days. This can be gotten at most feed stores. Possibly she has some internal infection somewhere else in her body which is causing distress. Also, if she has found that she would just rather eat eggs and oats, then that may be all she will eat anymore!
Apple cider vinegar is a great thing to use because it will help to balance the ph of the entire body of the bird helping to fight off bacteria and fungus, and increase her appetite. It is mixed 3/4 teaspoon per one quart of water, plastic waterer only, and changed and made new daily.
Maybe even some probiotics in the water will help with good bacteria in the gut and crop and maybe stimulate her appetite, but I would try the ACV first.
Are you feeding a chick starter feed? You can also post this question in our Raising Chicks Forums for a lot more help should these suggestions not help...
https://www.backyardchickens.com/f/11/raising-baby-chicks
Good luck with your baby! I hope she makes a full recovery.
