Hi, welcome to the forum, it is important to rule out respiratory system dyspnea (breathlessness) from cardiovascular dyspnea. Or else you may have more than one problem contributing to the breathing discomfort.
The most common causes of dyspnea are asthma, COPD, interstitial lung disease, and cardiomyopathy, valvular disorders, pericardial diseases, anemia etc.
You need to undergo pulmonary function tests like spirometry, chest radiograph and ECG to rule out the cause.
It is difficult to come to a certain diagnosis with available history. Once the diagnosis is made measures can be taken to prevent breathlessness. Such as allergen avoidance, short acting bronchodilators in respiratory causes. As for cardiac causes medications are available to prevent further worsening of symptoms.
Further evaluation is needed. I suggest you to consult physician. Take care and regards.
Sounds like possible exercised induce asthma or cardiac issues. You should difinitely consult your doctor for a work up and evaluation.
Take care.