KIds with allergy, especially uncontroled ones, are common candidates for frequent nosebleeds.
Prolonged shortness of breath and chest tightness, indeed can be symptoms of exercise-induced asthma.
They usually begin about 5-20 minutes after starting the exercise, and are most intensive 5 to 10 minutes after stopping the activity.
Some people get asthma attack only triggered by exercising, and no other triggers.
Sports and games that require continuous activity or are played in cold weather are most likely to trigger an asthma attack.
As an allergy sufferer you are more prone to asthma, or in other words, hay fever can predispose someone to asthma.
Asthma may appear for the first time during adolescence (more commonly in girls).