Antibiotics

My boy is 5.5mths, and caught a pretty bad cold that started on Apr 23. We went to the clinic 4 times in the span of 8 days as his conditioned kept worsening after each visit. Finally, yesterday, the doctor prescribed him with antibiotics and also hydralate because my boy was vomiting due to intense coughing plus his dislike for the other mid ones, and he was dehydrated. I was wondering if any mummies here have had the pain of having to give your baby antibiotics before he/she turned 6 months? Is it really safe and alright for such young infants? I’m just worried at the side effects, even though the doctor said it was fine. I just find that drugs are generally not fine, especially when their kidneys & liver are not so well functioning yet.