It's more than likely that the arguement with your parents got the adrenalin flowing and the symptoms you describe can be attributed to the dump of adrenalin in your system. This does not mean you now have an anxiety disorder. More likely this was the first time you were really aware of the after effects of adrenalin on your system. Adrenalin is known as the "fight or flight" hormone.........it is what ramps us up to prepare for either fleeing from an enemy or fighting them. If we don't have to flee or physically fight, we are still left with a lot of adrenalin in our system and while it is being absorbed, it can cause the symptoms you speak of. For those of us with real anxiety or panic disorders, we get that adrenalin rush for no reason and the symptoms include not only the ones you've described, but can include numbness in fingers and around the mouth, a horrible feeling of impending death, we can feel ice cold or sweat, our heart rates can go off the charts and our blood pressure can reach frightening levels, we can experience what is called depersonalization or derealization which is hard to explain, but it's like nothing is real anymore and it's a very scary feeling.........the list of symptoms could on for pages, but I'd say that you did experience some anxiety after the arguement which would be normal if you normally don't fight with your parents or if this was a particularly nasty arguement.
I would say that this was probably a one time event and you should just put it behind you. Dwelling on it is just going to reinforce the concern this caused you, which was strong enough for you to write to us..........I think the vast majority of us would say "let it go."
The one thing I will say that even while being short of breath can be very common in anxiety attacks, if you notice yourself getting short of breath at other times, let your parents know immediately! I don't want to scare you and I truly believe your shortness of breath was due to the emotional aspect of the fight, but it could be a symptom of asthma.
But please don't dwell on that either or start to Google symptoms of asthma.
You're fine. I'm sure you just got too worked up during the arguement.
If you have any other questions or concerns, just write again and hopefully someone not as long winded will respond! (You should hope!)