How can I tell if I have asthma or if I'm just really out of shape?

See your physician. This can be a very complex problem to understand. Being out of shape can be one reason but lund disease ( not just asthma) and / or heart disease could be the culprit. Some metabolic disease like thyroid problem can also make you short of breath. This is a problem that really needs to be discussed with with you pcp or allergist.
Doctor visit. Since both alternatives need medical attention, you should visit your doctor. Both can exist together. Shortness of breath is significant and should be addressed by your doctor.