A cold and cough while breastfeeding is usually a simple viral infection, and it's safe to keep feeding your baby through it. You don't need to stop breastfeeding for this.
Next Steps
Steam inhalation, warm fluids and rest help the most. Plain paracetamol for fever or body ache, and saline nasal drops, are generally considered fine while breastfeeding, but check with your doctor or pharmacist before taking any cough or cold combination, since several contain ingredients not suited to lactation.
Health Tips
See your doctor if the cough lasts more than a week, you develop a high fever, or breathing feels difficult.