Over the past several months I've experienced wheeziness and shortness of breath. After research on the internet I believe I might have mild intermittent asthma.

When I went to the doctor I told him what my symtoms were but he didn't seem very interested in particulars. He said I should come back to him when I was actually experiencing symtoms. I found this very strange. Surely, this isn't the correct way of diagnosing asthma, is it?

(He did check my lungs with a stethescope and with a peak flow meter. They were fine.)

A methocholine challenge is the way to diagnose asthma. It doesn't matter if you are having symptoms at the time or not. I would ask to have this ordered. It is easy and not very time consuming.
hope your dr listens to you and hopefully you find out.

Did you go to a pulmonologist? That's who you should see.