It's important to remember that family history does not necessarily mean genetic. If several generations were heavy smokers for example, yet you've broken the trend, this can cease the family link. Lifestyle accounts for a lot with the heart.
You mention cardiac tests, but have they done any pulmonary function testing? Are you active or not? Is there any reason to wonder if you have copd? Just a few other things I would look at, too. A lot of my shortness of breath is from copd, and then there are the times that my heart causes this.
I think that if you know your doc, trust your doc, and he/she gave you the green light is would definately relax a little. As far as family history goes....the only part that would directly effect you would be a couple off of the top of my head....one would be that if anyone in your family has had a heart attack at age 50 or younger you are in a higher risk group...it does not mean that you will have one..just that you are in a higher risk group and need to have a doc stay proactive w. you thru regular exams....clotting issues in your family hx. is also a factor as well in relationship to the heart. I tend to side w. your doc just from the position that he or she is just that a doctor...as i have seen few if any responses on this site where a doc weighs in altho it may happen on occasion. For the most part the individuals that respond on this site may have gone thru the same thing as you have and can relate to what is happening to you....it is more personal insight altho there are some medical professionals who do respond who have direct patient care experience in a medical setting but you need to look at their backgrounds to differ from who is who on their profile. There is no replacement for your doc at all ever...they know every little thing about you, your med. hx, the meds you are on, the risk factors, your lifestyle...all of it comes into play. I hope this helped a little bit