A dry cough that continues for a few weeks after a viral infection is quite common and is usually due to irritation and increased sensitivity of the airways (post-viral cough), rather than an ongoing infection, which is why antibiotics like azithromycin often do not help at this stage. The cough typically improves gradually, but you can manage it by staying well hydrated, using warm fluids or steam inhalation, and taking simple cough suppressants or anti-allergy medicines if there is associated throat irritation or allergy. Avoid smoke, dust, and cold air, which can trigger coughing. However, if the cough lasts beyond 6-8 weeks, worsens, or is associated with symptoms like fever, breathlessness, wheezing, or weight loss, you should consult a doctor for further evaluation (such as a chest examination or X-ray) to rule out other causes like asthma, acid reflux, or secondary infection.