What Remedies Are Safe And Effective For My Toddler’s Persistent Throat-clearing Cough And Recent Wet Cough?

My four year old grandson has had an upper respiratory cough for many months. It is like a little cough, like clearing his throat all the time. Now he also has a cold, so the cough is deeper and wetter. It is like he has two coughs. I have some remedies here as part of a home kit but am not sure which one to give.