Drink more fluids. Water helps loosen mucus and soothe an irritated throat. Dry, hacking coughs respond to honey in hot water, tea, or lemon juice. Do not give honey to children younger than 1 year of age. Elevate your head with extra pillows at night to ease a dry cough. Try a cough drop to soothe an irritated throat.
That is actually true to a certain extent. Most of the time you need to have some sort of sensitivity/allergy to dairy. But dairy products can increase the thickness of your phlegm, therefore can clog up your sinuses, and eventually cause the sinus pressure.
1 Too much of a good thing can actually be a bad thing.  You have congestion, runny nose, phlegm and frequently clear your throat. Dairy is a mucus forming food. The root cause of mucus is inflammation in the body and inflammation is the precursor to all disease.