Lung capacity

I just started Crossfit and I love it, I am just really out of shape. Each workout they make me run, but I have at least 60 pounds to lose still so running is very difficult. After my workouts, my lung have just really hurt. I cough and cough and it burns. I don't smoke or have asthma, all I can think of is that my lungs are just weak. Any suggestions? Will this pass once I am training 3x a week for awhile?