I've been where you are and can sympathize. First, have you been checked out by a doctor and given an "all clear"? If so that is GREAT news and you take comfort in that.
Second, don't kid yourself. We will not be immortal - won't happen. Remember Barney Clark? In 1982 he was the world's first artificial heart recipient; he lived about 112 days (I think thats the number) with a mechanical heart. It was touted as an amazing medical breakthrough which would usher in a world where faulty human hearts are removed and replaced with nice, efficient mechanical ones which would never fail. That was over 30 years ago and I don't ever hear of anyone today being given an artificial heart. Those of us with heart issues need to come to terms with the fact that, at some point, no matter what the cause of death, our hearts will stop beating and we will die.
You said that you read that hypochondriacs handle serious illness better than other people, that may be but we suck at handling the rest of life because we're so wrapped up in thinking everything is a serious illness. We make the life we value so much miserable by constantly worrying that we'll die all the time.
You can only die once, but you get to live every single day. Don't spend the living days worrying about that dying day.