Chickens do not get colds. They get respiratory diseases, which can sometimes be very serious, and will often infect the whole flock. Seperate your infected bird immediately. Keep her warm, well fed, and hydrated. Give her electrolytes and probiotics if you have them, as this will help her immune system. If the disease is viral, this is all you can do for her.
A more serious case would be if she has Chronic Respiratory Disease, Coryza, or another type of bacterial respiratory infection. To treat one of these diseases, get Tylan50 or Tylan200. Weaker antibiotics, like Oxytetracycline, may work, but in my experience, they do not. If using Tylan50, give your hen .5 ccs if she's a bantam, 1cc if she's a large fowl, injected into the breast muscle for three to five days. The dosage for Tylan200 is .1-.3ccs for a bantam, .5ccs for a large fowl.
No matter what respiratory disease your chicken has, she will likely be a carrier of it for her lifetime. She may show symptoms again, especially during times of stress, even once it has been treated.
I hope I've helped! Your chicken doesn't seem to be too seriously infected, but just keep an eye on her and the other birds. Make sure to isolate her and give her supportive care. Hopefully, she recovers fully.
