You might think about starting her on an antibiotic.
That's what I do when a chicken turns up with symptoms such as yours has.
The first sign of trouble is that they go mute. Then they park themselves, like a zombie, barely moving, with tail held low, and eyes closed, dozing off.
I have one now that was like that six days ago. She's responding to the amoxicillin I'm giving her and is almost back to normal.
I have another hen who has recurring infections that cause her to behave in this manner. She gets started on the antibiotic the second I notice her doing the zombie act.
When you get used to the signs of a sick chicken, you can more often than not make them well again if you catch it early.