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Since you have cough for 2 months now , you should get an x-ray of your chest done , also get your Phlegm tested , to rule out infections like Tuberculosis
Since you d onot have fever
or any change of color in sputum, I dont think there is any infection present , but just to be on the safer side....
For chronic cough
you can try homoeopathy safely, and even for allergies it works realy well.