Hi and my regards,
After going through your query, it seems that you are having an allergy
since you get cold and some chest congestion when exposed to cold air. Your doctor was right when she gave you the anti allergic medication. Considering that you are having greenish phlegm, I would prefer an anti biotic like azithromycin
500 mg once daily before meals for three days along with the rest of the medicines, especially if you are also having fever
and throat pain. If fever is absent you may take only the anti allergics. Your problem can also be prevented if you take care not to sit in the cold air or get wet in the rains. Do not have cold or sour foods for a few days. Have warm water gargles and home remedies
like a spoonful of ginger juice and honey. You make require consultation with an allergy specialist in your area if the cold and cough
increase in frequency.
I hope you get well soon.