Hello This type of severe cough as you mentioned in the query may be due to : 1 Infection , for which your doctor prescribed amoxyccillin 250 mg , so continue this medicine for another 5 days . 2 Allergic bronchitis may be the another cause . When such patient visit I advise them to take montelukast+ fexofenadine tablet one or two in day depending on the severity of symptoms . But if breathlessness , whistling sound present ( during inhalation or exhalation ) I advise my patient to take montelukast+ bambuterol tablet , one or two . 3 I also advise my patient to take codeine+ chlorpheniramine maleat syrup for sever cough . But this syrup is a habit forming drug so use it only in emergency and give you son under your guidance. Hope this will help you. Hot coffee and steam inhalation also help in such type of case. Good luck.