I know how it is to feel for an animal that is obviously in a bad spot. But next time let your heart think about the birds you already have at home if you have an existing flock. You can really bring home a lot of ongoing problems and heartache to what was previously a healthy flock. Whatever this is it's going to be very, very easily spread. You could maybe be lucky and this is coccidiosis or worms, but the runny nose suggests otherwise.I know. Bad idea. But my heart could leave the chicken there. So, I brought her home.
Doesn't appear to have mites.
Poop looks fine.
Coloring of comb is fine.
However, she won't do anything but stand up, sleep, with head tucked in wing. She's obviously sick. Can I help her?
I would probably cull this bird and disinfect like crazy, cross fingers and toes and hope for the best. If she has already been around your birds, or even near them, it is to late, they have been exposed. If that is the case you'll have to decide if you want to treat her and keep her or not. Also watch your other birds like a hawk for any symptoms.
If you can get your hands on some Oxine AH I would spray all around your coops and put some in the water. I have used that in the past when we had an outbreak of infectious bronchitis and I do swear by the stuff. It is antibacterial, antifungal and antiviral. If you get some be sure to use it as is, UNACTIVATED.
If it does turn out that this is a respiratory disease and you start having multiple birds show symptoms it's best to treat with antibiotic's as Eggcessive mentioned. You won't cure the disease but you will help prevent pneumonia and secondary bacterial infections that will kill your birds. Any sick birds that recover will remain carriers of whatever this is.
Good luck. We've been down the respiratory disease road here, it's no fun.