Hi and thank you for choosing HCM to share your question. I read carefully your question and understand your concern. Your cough is considered still acute since has only three week.The most frequent causes of acute cough are viral infections which in general are mild and self-limiting.In some cases it can be complicated by bacterial superinfection and if this happened you needed antibiotic as your treating doctor has prescribed. In the setting of sinusitis and gastric ulcer,even a simple viral infection causes more pronged cough. What kind of antihistamines did the doctor prescribed?Are you taking medicaments for your gastric ulcer? Newer Antihistamines like Desloratadine,levoceterizine may help in allergic rhinosinusitis,but not other forms of rhinosinusitis.For other forms is better older class of antihistamines such as chlorpheniramine/dextrometorphan. You need also a proton pump inhibitor such as pantoprazole if you are not taking one, since the acid of the stomac tends to come up in the esophagus and irritate the bronchial tree and so contributes in prolonging cough. I hope my opinion can be helpful to you. Kind Regards Dr.Dushi.