Well done - you're getting there. How often are you running?
That's something that I'm running into right now. I run in between my strength-training days, and I'm really concerned with my schedule. It always depends for me on whether it's the middle of the day or late at night (I'm always outside), and the humidity can get to me at times, as well.
A little story:
About seven years ago, I couldn't go a mile. I would start out running and tire out very early on in the run. Never quite figured out what was going on - I was very physically active, played tennis at least once a day, and was in pretty good shape. I think the most likely candidate was the pace that I set for myself. At any rate, I put the mile down for a while and came back to it three years later with a larger group than before (an entire class versus those trying out for the tennis team) and I trained for a bit and beat every one of them with a 5:16. Got no idea what time I run one now, but that was a good day.
As others have said, though, a lot of it for me is mental. I run from my house to a track, and I just go until I think I'm too winded to go on any farther. Then I go another lap and sprint through the back stretch. Then I stop, stretch, grab some water, and walk/run home. Once I reach that mental limitation, the best way to push past it for me is to just forget the pain and extremely heavy breathing and go until I just. can't. go. any. farther. It doesn't feel particularly good physically, but the mental kick is more than worth it.
Keep us posted.