In terms of skin (I give you my perspective as a dermatologist) long term use of antibiotics for acne is considered over 12 weeks.
The main harm in long term use of antibiotics is that it alters our normal bacteria and fungi.
I am sure that your pediatrician is weighing the pros and cons of treating your baby vs him getting sick. But, it should be something that you carefully discuss at your next appointment.
I hope that helps

Dr. Mohiba Tareen
Tareen Dermatology, Roseville, Minn
Castle Connoly's America's Top Cosmetic Dermatologists
Adjunct Assistant Professor Univ of MN Dept of Dermatology
www.TareenDermatology.com