Hi Doctors,,my Son Is 3month Old Had Cough,can Not Sleep

Hi doctors,,my son is 3month old had cough,can not sleep well at night ,no fever and breastfeeding well
The doctor diagnosed that there is bronkolitis and prescribed suprax(cefixime),my question is is this antibiotic is safe according to his age and what your advice
His birth weight 2.5
Current weight 5.5
Thanks