My son has been taking antibiotics. about 3-4 times already. He's more frequently on Zithromax. And he tried Klacid once.
It is completely safe as long as you complete the course of medication.
Some forms of antibiotics (like Augmentin) can cause diarrhea or runny stools. It is ok but you must hydrate your baby well.
It really depends what is causing the cough in your child. If it is viral, antibiotics will be of little help. Even so, if you start, you must complete the course.