Your persistent symptoms, of productive cough, congested chest and "rattle in one lung", are not typical of asthma. These symptoms are much more suggestive of incompletely resolved pneumonia. A lung infection can trigger asthma but the symptoms of asthma are never limited to one lung, and failure of pneumonia to resolve always warrants further investigation.
You should have another follow-up x-ray, now. The prescription of Symbicort® (budesonide/formoterol fumarate dehydrate) Inhalation Aerosol does not mean you have asthma. It only means that your doctor suspects that you might have it.
Given that it is now nearly 4 months since the bout of pneumonia, you deserve further diagnostic evaluation by a lung specialist. If the signs are truly localized to one lung, the one that had the pneumonia and especially if a current x-ray fails to demonstrate complete resolution, the lung specialist will probably suggest that he/she perform bronchoscopy and/or a CT scan of the lungs to determine the reason for this lingering problem. Also, this specialist may want to rule out the diagnosis of cystic fibrosis, with or without the diagnosis of bronchiectasis.
More antibiotics or treatment of presumed asthma is not what you need at this time.
This Could be Astma.Ask for A Lun Function Test