I don't know if specifically enlarged hearts are hereditary, but the risk for cardiovascular disease, in general, is.
Testing for diabetes and hypothyroidism is standard if you complain of persistent fatigue. I have been tested for both, rather regularly, since I was about 21, because I have a family history of diabetes and I have persistent fatigue. More recently a family member developed thyroid disease, so I get to look out for that, too. Luckily, I recently began treatment for a different condition, and that seems to have alleviated much of the fatigue.
Just a thought -- if right now you now feel your heart racing, it's probably the anxiety you're experiencing. That's called palpitations, a somewhat normal response to anxiety, so just relax... take a deep breath... you'll be fine.