Wow, that's ambitious, if you don't mind me saying so. I took up "running" a couple of years ago, and in between injuries (nothing major, but something wonky with a nerve in one of my feet) I have taken sporadic breaks and decided not to be so regimented about it.
At no time have I EVER run a pace as fast as yours. Not even close. Even when I was running 5k distance with zero walk breaks at my peak (having trained in high humidity and temps b/c of where we live), I never have been faster than 13.5 min/mile.
I know that is terribly slow, for someone contemplating a half. But, maybe to start out with, you should lower your goal to something more reasonable for a newbie. You didn't say how long you had until the half race day, but it sounds like it isn't far off if you are pushing yourself the way you are.
Never increase your distance more than 10% per week or you risk injury. And running vs an elliptical is very different. Number 1, impact. Can you say shin splints? Yeah... want to bring your running to a complete halt? Keep adding distance at that pace without regard to any actual plan.
And it really is all about the breathing. Go to Runner's World.com and you will find links to training for various length races and for various runner conditions (newbie, post-injury, tri-athlete, etc). There are links and articles about breathing. Breathe too fast or too shallowly (this usually means too fast, also) and you will get cramps. You can also help yourself by breathing on alternate foot strikes. There are articles and theories that continuously taking your breaths on the same foot strike side increases the "trauma" to that side as you inhale. So inhale on opposite foot strikes. It takes work/practice, and a lot of concentration on your pacing.
Awesome that you are so motivated... but slow down. You'll injure yourself and not be able to run at all. It's not worth that.
The best way to work on your breathing is to run with no music at all. None. Just listen to your body and your breathing with NO distractions of "accessories."
http://www.runnersworld.com/the-starting-line/how-start-r...
http://www.runnersworld.com/training/half-marathon-traini...
http://www.runnersworld.com/half-marathon-training-plans/...
http://www.runnersworld.com/runners-stories/running-my-fi...
http://www.runnersworld.com/the-starting-line/how-run-non...
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