It's really hard to answer this question over the internet. This is something you might be better off discussing with your physician as he or she can see you and interview you personally. 

That said, I'll try to answer it based on my own personal experience with asthma.  

If you are getting short of breath to the point you are needing to use your rescue inhaler, then it's possible it could be your asthma.  If you are just getting winded while going up stairs, and then you feel fine with rest, then this is probably just being out of shape. 

However it could be a combination of the two. I have noticed when I go a long period of time without exercising I seem to get more winded going up stairs and such than my friends do who are equally out of shape.  My theory is this is because I have asthma and they don't.  However, I could be wrong.

I find that when I exercise regularly I do not get winded no matter what I do (or at least most of the time).  I believe this is because, as science has proven , exercise makes both your heart and your lungs stronger, as well as giving you more energy. 

That is also why most asthma experts recommend all asthmatics exercise to some extent no matter how bad their asthma is.

In case your interested I expound upon this topic in the following posts:

Come on asthmatics!  It's time to exercise

Even we asthmatics can run