I'm not 100% positive, but I don't think Mucinex is supposed to be used on kids that age.
As an adult, I took it. It helps.
In my 7 year old daughter, I used it once and it helped.
there is a brand called "little noses' which is for congestion/stuffiness. It is made for kids this age. You can find it at most drug stores.
Liquids.. and hydration is important to keep mucous secretions thin and productive. Orange juice however, will make the mucous worse.
Water is the best.
Benadryl, will dry out the mucous secretions. That is how it works, as an antihistimine. It does not necessarily help with coughing per say. Coughing... can be either because of a chest cold... or because of post-nasal drip... as the mucous drips down the throat, it causes one to cough. SO... the "origin", of the cough, is important to figure out. AND... I hope the Doctor checked her chest... to listen for congestion etc.? If her chest was clear... then most likely the "cough" is not chest in origin.
Liquids, water, is the best for thinning the mucous.
You can also try putting a warm compress/heat pad on her chest... this helps the chest and coughing. Cold air... will make it worse.
I would, take her for a follow-up with the Doctor if her symptoms does not improve or if it gets worse, or continues.
All the best,