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.
The common cold is a viral respiratory infection causing sore throat, stuffy or runny nose, headache and more. A middle ear infection puts pressure on the eardrum, causing pain and, sometimes, hearing loss. Exposure to smoke can cause coughing, wheezing, shortness of breath, chest tightness, chest pain, and more. Dust exposure can cause congestion, runny nose, cough, shortness of breath, tightness in the chest, and more.