Talk to General Physician on Baby Is Having Cough

Salam, is there any peds available? my baby boy is almost 10 months old and having cough, can't sleep peacefully. we went to ER at Children hospital Karachi, there was a doctor who checked his chest and gave him anti-biotic saying he is having mild chest infection. we were not satisfied with the doctor so we went to other hospital, there was another peds doc there who checked him throughly and said he is having mild chest infection and mild sore throat. and she also give him anti-biotic incase he is having a fever. and also give him acefyl.. but I am also not sure about it. can you please tell me what to do? should I give him anti-biotic or not?