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.
Sinusitis usually follows an upper respiratory infection (such as a cold) or an allergic reaction (such as hay fever or allergic rhinitis). These can cause inflammation and swelling that prevent the sinuses from draining properly. When sinuses become blocked, they provide a place for bacteria, viruses, and fungus to live and grow rapidly. Although a cold is most often the culprit, anything that prevents the sinuses from draining can cause sinusitis.