One idea that I heard, and it makes sense to me, is that the reason winter is 'flu season' especially in the northern parts, is because of the dry air. Aerosolized virus's find it easier to get around in dry air, whereas if the air is kept more humid in the winter, not only is it more comfortable for humans, but the virus's can be trapped by water vapour and fall to the floor much more quickly than they would in dry air.Thanks for all the wonderful advice. The dry cough that seems to be 'stuck' in my upper chest is the only symptom. I thought syrups and so would not help, because the cough is not throat related, but more to my trachea. My doctor was advising tea and honey, so I will take his and your advice first.
About dryness of the air: that could be valid too. The atmospheres has been really dry for a few weeks now, and because of the relatively cold nights the heating system is still working quite a bit.
If it is possible to humidify your air in the winter especially, not only may it reduce the chance of catching a virus, but you'll avoid dry skin, etc.