Don't run everyday, don't run the same distance or the same pace. Break up your routine and slowly increase the workout. Like run one or two days a week for distance, a couple of days varying the pace and one day a week you run 2 miles for time then some easy pacing to build up stanama. I'd suggest training for 1/2 hour a day for 4 days the first week, the second week, 45 minutes for 5 days, 3rd week 1hour/5days, 4th week 1.5 hours/ 5 days. The day before your "Test," relax, don't run and eat lots of pasta. Be sure to hydrate yourself the whole time!
Start out running a mile the first week each day and work up to over 2 miles by the end of the second week, after that run at least 2 miles each training day. You don't have to run the entire workout but do exersizes that keep your heart rate elevated. Keep track of your heart rate ( the 220 minus your age thingy). DO NOT OVERTRAIN! If you push yourself too much you'll hurt yourself instead of improve and might blow up on test day.
A Month is a little short on time but if you already have an exercise program now the shift to running shouldn't be too bad and you should be able to do it. Hell, you might be able to hit your goal in the 3 / 4 week.