Beginning aerobic exercise -- tips?

So my doctor recommended that to lose weight, aside from the standard dietary changes I should also look into aerobics. My favorite kind of "exercise," just because it doesn't particularly feel like it, is dancing -- by which I mean the kind you do in your room when no one's looking. The problem is that this doctor also says that the most strenuous part of the routine should last around 15 minutes. I'm lucky if I make it to ten, and even at that I feel like my heart's about to burst. I know it's just because I'm not used to it -- I'm 22, and aside from being overweight I'm actually not in bad health, so it's not likely I'm going to drop dead of a heart attack or anything. But is there any way to get in that level of exercise without feeling like I'm dying?