Hi, Thanks for your query. Get a chest xray done. Many a times upper respiratory tract infection may involves the lower airways also and may require antibiotic to cure. Cold that persists longer and associates with symptoms of shortness of breath may have underlying asthma. If your breathlessness persists or you wheeze at night, or you have history of allergies to dust, fumes, etc or if their is family history of asthma positive.......then must visit a chest physician for proper diagnosis and treatment.... Best wishes