I recovered from covid but still have this cough that gets worse when moving is this persistant cough normal ct scan showed just a little bit of damage from the virus but dr is not concerned about it, will my lungs heal?will this cough ever go away?

At least in the early days of covid at least 50% of patients studied had abnormal chest CT scans even without respiratory symptoms. Your CT apparently did have some evidence of lung involvement. If your oxygen saturation is normal& you have no chest pain or shortness of breath, I would only take a cough suppressant.like DM syrup to cut down an annoying dry cough. Continue deep breathing and moving

Some causes of the prolonged cough including bronchospasm, areas of scarring and secondary infection may be considered. Pulmonary testing often provides additional information. If the cough exceeds 5 weeks, a Pulmonary specialist may be helpful in determining the next step. Please provide additional details about the scan.