Thanks for your questions.
I feel your inconvenience for these continuous
cough and
allergy.
If I were your treating physician,I would look for details history like
>Cough : Productive or not?>
Smoking habit, > Allergy : dust,
cold or any other particular allergens,> History of
fever,>Breathlessness etc.Then I would perform some physical examinations specially your chest.Since you have been suffering from cough despite of having syrup for 2 months,I may advice few laboratory investigations.After confirming diagnosis I would suggest medications.
> For your second query: You may try to find out the cause of your allergy yourself like dust,certain food,occupational environment etc.Then try to avoid those conditions first.Use anti allergic medications if required as per your physician's advice.
So my opinion is : Consult with a respiratory medicine specialist.
Take care and get well soon :)