Don't know if anyone covered this, but one of the first things that you said was that you were going for a 2 mile jog everyday. Thats a damn good start in my estimation if you are actually sticking to it.
Honestly, I can understand how hard it is to make time for exercise, but in your situation, it sounds like you have to. Keep this in mind as you are working out. First off, try and stick to cardio, it's going to give you more of a weight drop than something like weight training, which if you are power lifting, you really aren't going to lose weight as much as turn your fat into muscle. Both are good approaches, but if you are going strictly by weight you're going to see more of a weight loss numberswise with a cardio exercise program.
Keep in mind this number if you really are committed...3500...thats the number of calories in a pound. So in essence if you can cut 3500 calories from your diet, you could lose a pound as you do this. The best method obviously, is to eat a bit less, and work out a bit more to work on that 3500 calorie number. Also, don't expect quick results from any diet, the name of the game is getting more healthy, and while weight is a predictor of that, you will be more healthy even if you lose only a bit and exercise more.
Lastly, eating on a budget is mos def something I know. Look into http://www.recipezaar.com/
they have amazing recipes that people submit and rate, so you know they most likely won't suck or be too difficult when you try them. If you love meat, try to stick to lean meats like chicken and turkey, this will lower your fat intake a great deal. If you are tempted by the atkins diet, I suggest against it, as do almost all dietitians. The simple reason that the Atkins diet works for so many people is the high protein intake. Protein fills you up quicker and longer than carbs, thus the real end result of the Atkins is that you are eating less, good...and yet if you only eat crap, that is going to affect your health regardless of diet. Once again, yeah you can lose weight on the Atkins, but you might actually be more healthy at a higher weight with a better diet. A great method to get a good deal of protein is to eat meals with rice and beans. By themselves they are an incomplete protein, but together they make a complete protein just as you would get from high fat meats.
Best of luck to you on your decision to attend law school, but honestly, law school aside, the decision to go on a diet and exercise is yours. I think it is good to heed your doctors advice and not attend if that is his best advice, but I kind of feel like that advice goes with the assumption that if you go to law school you will be devoting too much attention to school and never be able to stick to a diet. So, ask your doctor if you stuck to a diet in law school if it would still be a good idea.
Just as others have said...I am no expert, heed the advice of your medical professional. Good luck with the decision!