Hi welcome to the health care magic
You are having viral and allergic upper
respiratory tract infection.. (diagnosed by your physician)
For your case i will recommend first investigate with CBC
If you are having viral infection
lymphocytosis can be seen and if having
allergy then high eosinophils seen in CBC....
For viral inflammation decongestant and if wet cough then expectorant can be prescribed (as you have been prescribed)
For allergic inflammation fexofenedine like drug better
In week your symptoms will subside... No additional cough suppressant needed
Take one tsp turmeric powder in hot milk daily
Avoid excess spicy foods
Drink warm water as having soothing effect
If after inflammation over and
dry cough not resolving or severe dry cough then only
dextromethorphan like cough syrup can be prescribed
Hope your concern solved
Take care