Yes. That is a symptom of respiratory issues. If she does have a respotiroy infection, it is very manageable. Do note that respiratory infections are not "treatable". You can treat the symptoms, but the infection will never go away, they carry the disease for life. You will have to treat with antibiotics every time symptoms arise.
I'm not familiar with antibiotics, but do keep her on that, she should improve. I would also feed a probiotic along with that. A favorite of mine is made for dogs, but its very high quality. This one-
https://www.googleadservices.com/pa...6yqb3AhUyITQIHaL-BkAQww96BAgBED4&ri=16&adurl=
A bit pricey, but it will last you a long time. Its also soil based, which is the most affective. Other lower quality poultry probiotics aren't soil based, and die before they reach the gut being ineffective.
Does she have any nasal or ocular discharge, bubbly eyes, swollen face? Those are all symptoms of a respiratory infection. Might help us determine which one your dealing with.
I'm glad you didn't choose to euthanize. With what I'm hearing I think this is manageable.
Do note that it means your entire flock has the disease, not only her.