This depends very much on the ingredients of the cough medicine, and even many over the counter options are not recommended. Certain ingredients, such as acetaminophen with codeine, pseudoephedrine and antihistamines, can severely reduce or even deplete breast milk supply within days, as well as have sedating effects on a nursing baby if enough doses are taken to pass through the milk. If you have any questions, get in touch with a qualified IBCLC and double check all questions about any drugs with your pharmacist.