Bronchiolitis? Happn with asthma too?

I have a chronic cough from 2-3 months(not that much but yes its there with mucus). Recently did an xray and pft, attached reports.. Is this treatable? I showed to a local pulmonologist, she said its fine treatable but i still want some reassurance... Please have a look on the reports.. History: I don't smoke(3-4 times a year, that too before lockdown, never smoked post that). I dont like smoking itself. I have a history of tonsil infection. I have ige level 440 Esionophils 10.5%. My mother is asthmatic.. Is early small airway obstruction linked to copd only? Or can happn with asthma too? The pulmonologist said definitely its not copd, but i hope its not anything else which is serious. My symptoms: cough with sputum, mostly throughout the day, more after eating/workout and when i get anxious. Please help.