Cough Medicine

my three-year-old has a pretty bad cough. Poor baby can’t get any relief, he’s thrown up from coughing. The medicines I’ve given him hasn’t really worked. Just curious on which cough medicines are good for three-year-olds that have worked for your little ones? I’ve tried honey. He’s very picky. He won’t drink it. I’ve tried hot steam from a shower. I’ve tried cold air. Nothing really seems to work. Took him to the ER last night, he doesn’t have anything serious going on just a bad cold, the doctor there just told me not to give him anything at all which I’ve understood in the past that sicknesses pretty much have to run its course. I’m just trying to give him some kind of relief. If anything helps, let me know please!