Thank you for the enquiry and keen interest in TCM. I am also sorry to hear about your experience.
Persistent cough without an apparent reason can be effectively managed using TCM herbal prescription. I see a lot of such cases in my practice.
After a flu episode, you may have exhausted your Lung qi, which is necessary for defense and recovery. Chronic cough arises and you may require longer than usual time to recover.
Such cases usually exhibit as dry non-productive cough or minimal phlegm that is difficult to expectorate. Phlegm is usually thick and foamy. The cough comes in periodic episode due to bronchospasm, patient commonly complain of itchy throat, or sensation of a foreign object in the throat.
According to my experience, the prescription consists of herbs which can invigorate Lung Qi (stabilize immune system), nourish Yin (replenish moisture and promote recovery), antispasmodic (to relax the smooth muscles in the airway) and phelgm dissolving (reduce secretion).
I hope you feel better soon!