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Fibrotic and hazy infiltrates on both upper lung zones is usually found due to healed lesion like that of tuberculosis
. Hazyness may signify active disease and should be looked in accordance with symptoms like cough of any type, bloody sputum, loss of weight, evening rise of temperature, night sweats etc. I advise you to go for sputum for acid fast bacilli examination which is readily available at designated microscopy centres.
The report reading ''The heart is not enlarge, Aorta is unremarkable. Both costophrenic sulci, hemidiaphragms and visual bones are intact'' just say about normal findings on chest xray.
Now regarding prolonged cough
. It can be caused by various reasons like asthma, pulmonary edema
, eosinophilic bronchitis
, acid reflux disease, chronic rhinosinusitis
etc. The differential diagnosis is narrowed down on the basis of clinical history and examinations.
You must visit a pulmonologist to get your mother examined properly ang to get a simple breath test called spirometry done.