1. There doesn't appear to be evidence of coughing linked with pupillary dilatation, but bronchitis
which leads to anxiety
can causes pupil constriction, i.e. when stress
affects the body, almost anything is possible.
2. Pharmacologically, treatment of bronchitis is with anti-cholinergic agents, which means cholinergic activity is responsible for most of the symptoms of bronchitis, and one effect of cholinergic activity on EYE is constriction of the circular muscle of iris
and causing miosis
[and hence it was seen during examination,causing pupils not to dilate]
since most cases of bronchitis are viral in origin or caused by lung irritants like smoke and pollutants, antibiotics are not preferred choice, unless secondary infection is likely possibility, thus a good treatment option is drinking lots of fluids and getting some sleep, along with a humidifier to relieve some of the respiratory symptoms, and a cough suppressant medication for tiring cough.