You do not have to "wheeze" to have asthma. It is common though but everyone experiences symptoms differently. it is possible it is asthma. symptoms, shortness of breath, coughing, wheezing, tightness to name a few. There are also different degrees of asthma. Your best bet is to get a Pre and Post pulmonary function test done. Your primary can order it.
Make ssure you tell him it was while you were playing sports. There is such thing as exercised induced asthma that will not show up on a regular PFT. An Exercise Test should be ordered if you find your symptoms only occur during times of activity.
~when in doubt, ask your doctor.