There are several reasons for having increased mucus and cough. Asthma is certainly one of them. The mucus could be coming from the upper airways (such as allergy problems or sinus problems) or it can be coming from the lower airways (bronchitis and asthma are two major causes). The first approach to this is to determine the site (upper or lower airway) and then the cause (allergy, infection etc). The diagnosis of asthma is a fairly specific one that should be made when a pulmonary function test is performed and reversibility is shown after taking a certain type of medication. Often the diagnosis is made when someone hears wheezing and this stops with the same type of medication. However, the best way is with a pulmonary function test.
Good luck.