What's wrong with my chicken?

[BabyAutumn]

Sounds like a severe case of mites. If a check for mites turns out positive, try dusting the bird and/or bathing them with dog lice/mite shampoo. Mites can be deadly (I speak from experience), so act fast!

I quickly searched some images and inspected beneath her feathers but nothing seems out of the ordinary, as of black spots or infections.

 

[Yorkshire Coop]

Since separated she's been drinking and eating much more. I am not sure how to check for an eggbound, nor do I know if she's been laying. Now that I have her enclosed, I'll know for sure if an egg appears inside.

That's great that she has been eating and drinking more since being on her own. Even though you may not have notice aggressive behaviour the others could have been bullying her out of food and water. This could easily be causing the symptoms she has.
Here's a good article on egg binding and the symptoms ~
https://www.backyardchickens.com/a/egg-binding-symptoms-treatment-and-prevention

I haven't checked to see if she has a egg stuck ? She layed a about 2 weeks ago. Her sister layed 1 everyday . She is drinking and eating ok . No separated from the rest .

How to check for a stuck egg ~ https://www.backyardchickens.com/a/egg-binding-symptoms-treatment-and-prevention
Has her eye been gunky or weepy? That combined with the rattle you here suggests respiratory infection which can knock them off laying for a while.

 

[BabyAutumn]

I've searched up about the egg binding, got the hen and did it. But there was no egg inside that I could feel. Went a few inches. Just a lot of poop covering her butt. Because there's no egg, I'm not sure what's wrong with her. She barely opens her eyes and seems very tired. Has been drinking, but just pecking at her food. She rests and walks almost like a penguin standing up, and only really lays down when she's on my lap or arm. We're gonna get a large gray tub, put in the food, water, hay, and place her in our basement where it's much warmer and quiet. We're also gonna give her a bath to clean her bottom. Any tips on that? Or any other guesses as to what's wrong with her? It's been like this for about a week, and I'm not sure how much longer she'll last.