Since your cough persists despite taking an antibiotic (amoxicillin/clavulanate), an antihistamine/montelukast combination, and a cough suppressant, please do not self-medicate further. A persistent cough can stem from non-bacterial causes like cough-variant asthma, acid reflux, post-nasal drip, or a post-viral cough. I highly recommend consulting your doctor for a physical examination. They may suggest a chest X-ray or spirometry to pinpoint the exact cause and prescribe targeted therapies like inhaled corticosteroids or anti-reflux medication. Meanwhile, practice steam inhalation, stay well-hydrated with warm fluids, and rest. Do not worry; post-infectious coughs are very common and highly treatable once the exact trigger is identified.