Here is a simple explanation about how antibiotics provide little benefit for acute cough as explained below. Consult with your doctor.
"When pneumonia is not suspected clinically, amoxicillin provides little benefit for acute lower-respiratory-tract infection in primary care both overall and in patients aged 60 years or more, and causes slight harms." - From The Lancet - Amoxicillin for acute lower-respiratory-tract infection in primary care when pneumonia is not suspected: a 12-country, randomised, placebo-controlled trial
From: Do I Need Antibiotics for a Persistent Cough? "In most cases, no. Recently, researchers reporting in the British journal The Lancet looked at over 2,000 patients of various ages with a cough lasting no more than 28 days, and randomized them to receive either placebo or a 7-day course of amoxicillin. Patients with suspected pneumonia or any of the noninfectious causes listed above were excluded from the study. The researchers found that amoxicillin did not shorten the duration of the cough, nor did it mitigate the severity of symptoms in persons of any age group, including the elderly.
Why? The answer is simple: Almost all cases of acute bronchitis are caused by a virus, and viruses don’t respond to antibiotics, most of which are antibacterial agents. So, in the vast majority of cases where a cough is the predominant symptom, an antibiotic won’t help." - OneMedical
Always consult your doctor. No medical advice is provided here.