If you want to lose some weight then you'd best also pay some attention to your diet. Try and reduce junk food and see what effect that has to begin with.
If you're that exhausted after runing a mile or km then, unless you're sprinting and pushing to the max, i'd say your fitness levels have room for a lot of improvement.
It all depends how much effort you want to put into it. You could always join a gym or join a club which offers a sport you enjoy.
Or else gradually build up the distance you run. If you can run 1 mile then try and add a little distance each time you go out and gradually build it up. To get real benefit from jogging i'd say you'd need to be jogging for at least 20 minutes, 3 times a week, if not more. Once you can do this you could try and increase your speed.
It shouldn't be difficult to get a book which will show you exercises you can do at home.