Hi there,This is Dr Basu, experienced Internal Medicine Specialist.I am here to address your concerns and provide great service.
Since chest xrays are clear, there is no infection involved.
Since steroids help, you have reactive airway disease or akin to asthma.
Inflammation in the airways can cause persistent cough.
Hence you should consider a daily oral steroid inhaler and anticholinergic inhaler like Ipratropium oral inhaler.
Lung function test should be ordered to confirm asthma. Best wishes,It was my pleasure to help you today.If I have answered all your questions, Please rate my response Excellent (click on the 5th star on top).Please bookmark my profile for fast, reliable authentic answers!This is the link to my profile:http://www.justanswer.com/medical/expert-mysticdoc/