Hi, this is probably a post viral cough comma just give some Honey warm Fluids and they should improve over time, consult your doctor if symptoms worsen

If mild,avoid unnecessary medicine and just give steam inhalations for cold and cough and decongestant nasal drops for nasal block or increased cough on lying down. Use paracetamol for fever if required. If not improving OR accompanied by other symptoms like wheezing or breathlessness or dullness and refusal to feed,consult your paediatrician for physical examination and treatment.