Antibiotics will not help at all if the respiratory problem is a virus, from mold fungus, or environmental. Head shaking is a way to clear the airway and nostrils when there is mucus or fluid being overproduced. If you have a trusted vet, call them to see if they would see your chicken. There are some antibiotics, such as Tylosin, Denagard, or oxytetracycline for pigeons or fish, that may be available if there is a bacterial or mycoplasma infection. Those usually cause more severe symptoms, are contagious to the others, and you would see swollen eyelids, bubbles or foam in the eyes. thick nasal drainage, rales or crackles, gasping, mucus dripping from the beak. I would not treat with antibiotics if more of those symptoms do not appear.
