Call your doc and be sure my doc says cough drops r ok and also Tylenol cold and a couple others r safe for me I'm 29 weeks but no your not hurting baby from coughing
I don't think you can hurt the baby by coughing, I also have a cough and I'm not sure about the cough drops but I've been drinking decaffeinated green tea with lemon and it helps soothe your throat and lungs