When I get caught up cleaning or keeping busy sometimes I feel a flutter in my chest and I feel breathless. What is this?

Abnormal heart beat. Go see your doctor and get an ekg for a better diagnosis. You will probably need some other cardiac tests as well. Meanwhile lay off of coffee, tea, and drinks with caffene. Cut out any smokes as well.
Flutter. Although a "flutter" invokes thoughts of an abnormal heart rhythm, it would be unusual at your age. Check your pulse, and if possible, your blood pressure next time this happens. Asthma can also give similar symptoms. If you are menstruating, you could be anemic and this could give you the feelings when you are exerting yourself.