DD, 10 months, has a chesty cough, twice in half a hour tonight she has coughed until she has been sick, exorcist style! She is already taking penicillin because she has an ear infection. Do I need to take her back because of her cough, or will the penicillin fight the cough too? She is very happy in herself and her temp has been normal since Sunday night. It was 40 due to her ear infection.