As regards the poo if it dose not sink completely into the diaper like urine then there's nothing to worry about. But if it dose please kindly give ors zinc has first aid before presenting your baby to the doctor in the morning

As regards the cough, cough is a viral infection that should be left to run its course it will resolve on its own with or without medication however if it is accompanied by other symptoms like vomiting or last for too long then you should take your baby to see a Paediatrician for proper evaluation and management