With a runny nose, I would be tempted to jump to respiratory infection which you will not get cured on your own.....I just had one of my chickens fall ill so I know what you are going through. Very luckily I found a vet in my area that knows chickens and put her on a course of antibiotics....if your chicken is no longer eating or drinking on her own, I would say vet time. Now. That's what made me go. Even after she got out of the vet, I had to use a dropper to administer electrolyte water down her beak...sick chickens will go downhill fast if they don't drink and eat...mites certainly don't help...they suck blood and weaken the immune system....respiratory infections can be dangerous because if it is contagious, you will need to keep a very close eye on the rest of your flock.....whoever sent you those chickens is horrible. Sellers should not be sending sick or weakened birds to people, that's wrong. I hop things improve, I'm really sorry to hear it....definitely keep her separated, watch your other birds and call a vet if you can...let us know what happens.
Sorry to hear...
