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.
Your headaches with coughing and sneezing sound like a problem cause tussive headache. This headache normally occurs intermittently in people without daily headache though. Tussive headache (or cough headache) is a severe headache that happens when you cough (or sneeze) Some patients with low or high spinal fluid pressre have similar symptoms to your headaches--a daily headache with more severe headaches with cough or some position changes.