My baby has a bad cough, should I be worried?

Yes, if not sleeping. Cough is a natural healthy response to rid lung passages of respiratory irritants--as long as it is occasional and not life altering. But, if your baby's cough is severe enough to disturb your sleep or hers, then further evaluation is warranted. Also, cough with fever, bloody sputum, persistent vomiting, wheeze, or breathlessness could signal a more serious problem. For these, call your doctor.
respiratory . If the bay looks ok (eats and sleeps well and does not have a high fever) you can wait and see but if the baby is having any kind of dificulty or she/he is very young you should call your pediatrician, keep it hydrated.