It could be said that mathematics is the language of physics. That is another way of better understanding what is physics. Numerical values, units of measurement, and similar concepts are all mathematical in nature, and are used to describe physical quantities in the most accurate and precise manner.
In brief: Cough headache. There are a couple of possibilities. Coughing can raise the pressure inside your head, which can cause pain sometimes. There is also a poorly-understood entity called the primary cough headache,  that is associated with coughing, straining, laughing, crying, etc.
But when you have a cold, congestion, or allergies, the amount of mucus can increase, build up, and thicken. The feeling of this mucus draining down the back of your throat is postnasal drip. It often causes a sore throat, coughing, and problems swallowing. See a picture of postnasal drip.