Should I go to my doctor about asthma?

First off, my family has a history of asthma. My mum has it quite badly, and has nearly died from it a few times.

Anyway, I've recently gained some weight around my stomach. I used to be verging on anorexic (thankfully I saw someone) so naturally I'm not a big fan of weight around my midsection, but I wanted to deal with it in a healthy way this time. I've always been very outdoorsy - canoeing, hiking, biking, rock climbing, skiing - so I'm not totally out of shape, and I eat very well. I decided to start running, as I'm from Canada, and I can't do most of the other things in the winter.

Today, I tried to go out for a run/walk. I started off running for about 1 minute, and I had to stop, but I was alright after a minute or two of walking. Next time I tried to run, I lasted 10 seconds before I was wheezing, tasting blood, and having intense chest pains. It took me about 5-10 minutes to catch my breath, and be able to breathe normally again. Even now, 20 minutes later, I still start coughing when I breathe deeply.

So, am I just intensely out of shape, or should I speak to my doctor about asthma tests?