I would go see a doctor and make sure you are healthy enough to be doing the exercises. My sister is anemic and it makes her tired and it causes her to have shortness in breath.... My brother has asthma and can't do most exercises without a lengthy warm up. The best thing to do is go to the doctor and find out what is causing you to have those symptoms.
It is not necessary that you have asthma. Peoples with asthma can get shortness of breath without exercise. Your problem can be due to obesity and high cholesterol levels. In my opinion you should start your exercise from minimum levels which don't cause shortness of breath and then slowly increase the duration. Longterm smoking can affect the lungs and can take many years to be come healthy.
A friend of mine had this problem. After extensive tests she found out that her heart was weak and was pumping only 12% of the blood that it should have. After medication she returned to normal. She is big on omega3 fish oil now for maintaining a healthy heart. Get a check-up. It's the smart thing to do.