4months old and sick

My son is 4months and 17days old.been coughing for a week r8ght after we got back from kl to kuching..kuching haze very bad.even when we only stay inside the house and mostly use aircond.my mother who is a god believer keep giving excuse for me to bring him to clinic and i told my sister and we went. Turns out my son had inflame throat and mucus.we went to a private clinic. Dr gave panadol,coughing syrup and antibiotic and suggest to do nab.i only gave my son panadol and coughing syrup because my sister say he is too young for antibiotic and the doctor so daring give antibiotic to a baby. he is fully breastfed.my sister said that her son took antibiotic since he is a baby which made him get sick easily because the body cant fight own its own. My question here is that,should i give him the antibiotic or not?