Thanks for the question.

Based on what you describe here I think it's time you sit down with your parents and have a discussion about your health.  If you need to print this off and show it to your parents. As you know, it is not a good feeling when you are having trouble breathing, and being short of breath is something you should NEVER ignore. 

Yes, it is possible what you have is asthma, but unfortunately we cannot diagnose you over the Internet.  I would highly recommend your  parents take you to your physician so you can get checked out, because only your doctor can tell you what is wrong with you and what you can do to treat it. 

Likewise, if he diagnoses you with asthma, there are great controller medicines to prevent asthma attacks so you should be able to live a normal active life.

You should tell your parents that most asthma experts agree that if asthma is diagnosed immediately and treated aggressively it can be prevented from getting worse, and can therefore be easier to control now and down the road.

On the other hand, if you do have asthma and it is left untreated, it is possible that lung scarring can occur that can make your asthma more of a challenge to control down the road. 

If you have more questions please ask.  And definitely let us know how things turn out for you.