DISCLAIMER: Never take medical advice from forums, especially not in lieu of consultation with your doctor!
I had a classmate in school, died on the basketball court, similar sounding thing. Until you have a doctor clear you (and perhaps continue to clear you, if this is something that has any chance of developing over time, and is not just a genetic thing), I would certainly not push hard, and would consider replacing (again, until you know it is okay to do so) your running and swimming type activities with things that won't significantly stress your system. It won't have the same magnitude of results, but I'd consider things like light yoga and even simpler stretching, perhaps in the morning, and meditation of some form in the evening.
The actual "workout" doesn't matter so much, though you'll be working on flexibility and strengthening your joints a little. The key thing is that you still have the mentality. Quite often one of the toughest things about working out is keeping at it, and setting aside a few minutes in the morning and at night to focus on the idea of working out, can be just as important. Plus, when you do get cleared by your doctor (hopefully!), you'll have maintained the, for lack of a better term, "inner technologies" to train smartly and effectively.
Now, that being said, I will point out that this is my own philosophy, and it is colored by years of competing and training/teaching martial arts. Plus, men and women tend to view training differently. So when I talk about "inner technologies" and stretching in the morning with "intent", my image of that concept is like the samurai standing in the violent waterfall for hours. That image, or the feeling behind it, won't necessarily mean anything to you. It's possible some of the others in here might have some input?
At any rate, learning to sleep well is another one of these things that I've found can have a huge impact on your health and fitness level, even when not working out. Used to be I'd sleep a couple hours a night, in part because of staying up for those GSL broadcasts. Landed me in the doctor's office. It's amazing how much drinking water, sleeping at a regular time (and to that 8±1 hrs most humans need), and an appropriate diet really does help.