It usually takes me a good 10 minutes just to get to an even breath - to find my groove.
I'm not a doctor or 'fitness consultant'. I'm just another exerciser... Here's what I've learned:
You need to slow down and work up to this. Start slower, even walking, and try adding in shorter runs of higher intensity - as in 30 seconds. When you start getting your heartrate up too high and too short of breath, slow down (but keep going) until you've caught your breath. Work on going a little faster and monitoring your breathing and heartrate as you go so you can see where you are. Do this for longer periods than 15 minutes. 30 minutes, 3 x a week is what I've generally seen recommended as a minimum for cardiovascular health.
As you get more accustomed to your new slower pace, and to adding in the higher intensity short runs (called 'intervals'

, you can start upping the intervals. When you can do 30 seconds, then get back to a decent breathing within a couple minutes or so, up it to 45 seconds or even 60 seconds. Give yourself time to get your breathing and HR back down between each interval.You'll be able to increase your pace over time this way without running the risk of overdoing it.
Just my $.03 worth.