Runny nose and loose stools are two different issues.Its common for newborn babies to have noisy breathing, but if the nose is running, some medicines may be required to be used judiciously, including nose cleaning and nebulisation.You may ask a specific query for specialist Dr santosh's opinion. Loose stools may be following the new milk ingestion even if it may not have been spoiled. Skipping the newly added food item and continuing with previous feeds may help settle in 2 days. if motions persist, 2 dangers are likely that is dehydration
and spread of infection if any. Ask if any details needed. get the stools tested , understand danger signs or symptoms in infants.