It's not a question about using antibiotic in newborns,it CAN and IS used,but it's not indicated HERE. If mild,stop all medicines and just give steam inhalations for cold and cough and decongestant nasal drops for nasal block or increased cough on lying down and give paracetamol for fever if required. If not improving in 3 days OR accompanied by other symptoms like wheezing or breathlessness or dullness and refusal to feed,consult your paediatrician for physical examination and treatment.