Two miles!? You’re going to have to run a lot farther than that. Runners’ World suggests that per mile running you will burn [.75 x (your body weight)] calories. The good news is that at your weight you’ll burn ~170 cal/mile.
The bad news is that you have to burn 3500 calories to lose a pound, over 20 miles in your case. 30 lbs? That’s over 600 miles if you don’t start eating more.
The good news again is that it can be done! I was almost up to your weight at your age when I began running, and over about 18 months I lost 50 lbs (I went from 220 to 170). I could only run about 10-15 minutes at a stretch when I started. I’d increase my runs incrementally until, after 18 months, I staggered across a marathon finish line. Yay!
But I think you’ll be disappointed if you expect to get into top shape in less than two months. Make a long-term commitment, take it step-by-step, don’t give up and look forward to being in whatever shape you want by next June.
I think you can discourage yourself if you focus too much on the results. Focus on doing it everyday regardless, and after a very short time of trying to get into running you’ll start to get high from it, sleep better, be in a good mood all the time, generally feel good and you won’t have any trouble keeping it up whether you lose weight or not. Hard to believe, but you’ll start to like it for its own sake.