Whats wrong with your 93 Geo storm gsi when im driving and your battery completely dies but the car still runs and starts back up when you get a jump start but still continues to die?

What you describe sounds like a bad battery since the car will run until you shut it off .It is possible that the alternator is not charging. Try this test, after a quick jump start when the battery is dead disconnect the positive battery cable, if the engine dies then the alternator is shot, if not then it is probably the battery. A better test is to put a voltmeter on the battery when running you should have about 14 or more volts, and when not it should read above 12 like 12.6. 12 or less is not good. A load test is the best. Take it to the parts store and they can test them both for free.