Unfortunately chickens do not get colds, instead they get respiratory diseases. This will be apparent through most google searches. I spoke to my vet and he was careful to caution me that most chicken respiratory issues are "herpes" like in nature; which sadly means they are carriers for life. That being said there are also issues that are not herpes like,the problem is that most are.
You can submit a sample to zoologix or have a local avian vet test her for possible issues. This is probably the best route to ensure she does not have an infectious disease that could infect others.
That being said, I have read all over the internet, including backyard chickens, where Tylan 50 injectible/oral solutions may be effective. Your choice on how you want to proceed. Just remember that antibiotics treat bacterial infections not viral, and that improper antibiotic treatments may result in antibiotic resistant strains of diseases.
Does your chicken have any other illness signs or symptoms, watery eyes/nose; raspy breathing, diarrhea? How long ago did this start?
Have you considered gape worm or impacted crop? Does she have a foul smell?