Is this a normal feeling when running???

I keep trying to run and I feel like its not getting any easier. I went to the park to jog a mile yesterday and almost died. I pushed myself to try to jog slowly most of the mile and I tried to control my breathing. It was chilly out, in the 50s, and my lungs started to hurt SO bad. It burned to breathe in the cold air then it just plain hurt to breathe. When I got home, I had this weird cough like I just inhaled a ton of smoke or something, I guess its wheezing. Is this at all normal???