Hi , Good Afternoon , My Baby Is 2 Month

Hi , good afternoon ,
My baby is 2 month old and having cough, which cough syrup should I give to him? He is breathing from his mouth too due to cold. From 2 days back I am noticing that his tongue is becoming blackish. Please tell is it an infection as many of them said that it may be some infection. Please tell how to cure it. Thank you for your advice in advance.