Ibn al-Qayyim gives us a remedy in his book on Prophetic Medicine, in the chapters dealing with honey and oregano. In the field of bee products, we find a very effective remedy, which is propolis. This is a natural antibiotic, found in syrups or capsules. However, to avoid taking it in syrups containing alcohol, it can be taken pure with honey and oregano.
What the science says: cough
What published research says about the remedies mentioned above, for context — the studies address material causes, but healing belongs to Allah.
Coughing
Honey is the best-proven remedy for coughing: the Cochrane review finds it more effective than no treatment and comparable to common syrups in children (Cochrane, 2018) (Arch Pediatr Adolesc Med, 2007), and a meta-analysis evaluates traditional plants against coughing (Forsch Komplementmed, 2015). Thyme, marshmallow root, plantain, inhalations, and humid air complement these. Precaution: no honey before age one; a cough lasting more than three weeks, with fever, blood, or shortness of breath, should be seen by a doctor.