I am not someone who tries herbs for remedies but when none of the medicines doc gave my daughter cured her severe cough and cold fast enough, I used " sithiraththai". Just add little to boiled milk and let it boil some more. It gives good flavour and taste. It stopped her cough in no time. Even adults in my family take this these days.
Came across this post just now. You could try home brewed remedies like
kashayam - tulasi, karpooravalli, chitharathai, etc. My Granny used to say
that a beetel leaf post every meal would rid you of gastric troubles, aid
digestion and fight cough. YOu could try beetle leaf juice in a mild
concentration as well.
You could try this for your young one if the cough repeats again. Take two pieces of pepper and some jeera, crush them and make a fine powder.Take one spoon of pure honey and add this powder to it and mix well. Feed this solution to your young one. Once in the early morning in empty stomach and once in the night before bed. Its a permanent cure.
As Sri110 has rightly mentioned, you could make a kashayam with tulasi, karpooravalli and beetle leaf. But this will make the solution very strong and spicy. Make sure if your kid will be able to handle that much spice at once. It sure works though.