Cough in 6 month old

So my son is 6 month's old and I took him to his doctor's last Saturday bc he woke up with a cough. She said he has a cold but also thinks he also has some kind of baby asthma (can't remember exactly what she said) so she got him a prescription of steroids and a nebulizer. He just finished the steroids but he still has the cough. (Not persistent but it still worries me). What can I give him for a cough? She said cough medicine but I can't find any for his age. I'm a ftm and I don't know what to do! I don't like him being sick at all!