Does anyone know what might be causing my shortness of breath problem (see details)?

I have this odd problem. If I go to the gym and exercise on a stationary bike, I have no problems. When I start walking home, I find that I suddenly have to breathe harder and feel a little dizziness and have to sometimes stop walking to catch my breath.

I sometimes have a similar problem when walking up stairs. I have no problem reaching the floor that I want, but sometimes have difficulty breathing after I stop climbing.

Does anyone know what might be causing this? Is it a heart problem?