"COUGH SYRUP" won't help to cure the disease. Is that true?

Sugar doesn't delay healing -- I don't know where you got the idea that it does -- but it's true that cough syrup is merely intended to suppress a cough while you have one. It doesn't cure a cough. That will happen naturally, if the cough is merely the result of a cold or something else minor.

If you have a chronic cough, cough syrup may suppress it, but you need to see a  doctor to find out what's causing the cough.

i'm not sure I believe in it. Honey is better, it is soothing to the throat.

I will cure nothing.