Need help :O

I want to start running as a sport, but just cannot do it for some reason. When I tried to run a mile on my school's track for gym, I had to stop after 1/4 mile, and even jogging/walking my fasted for the rest took me a total of over 12 minutes.

I can sometimes run a full mile or more on a treadmill with moderate incline at around 4mph, but several times I ran half a mile at the YMCA, and afterwards I had to lie down on the nearest mat because I was about to faint (seeing spots and feeling dizzy). I also tried running around my slightly-inclined neighborhood, but got about 1/4 mile in before I had to stop because I was wheezing.

I know I don't have asthma, and I make sure to eat a good meal a half hour or so before I try to run. What am I doing wrong? I'm 5'2" and about 115 pounds - could the fact that I'm heavy for my height have something to do with this? Please help!! What am I doing wrong!