This is actually something that I've gotten through, though it took a couple of years. Just like some of you, it started with a racing heartbeat (I thought). That started the anxiety about my heart. I was obsessed with checking my pulse and such, and eventually went into a panic attack that sent me to the emergency room. I was told everything looked normal and to see a cardiologist. I saw a cardiologist and was told I'm fine.
The good thing is that through all of this I learned what the normal behavior of my heart is and how my actions can change what it does. Here are some tips:
1) Your breathing controls your heart rate. If you breath in, it beats faster. If you breath out, it slows down. Don't expect a constant heart rate, because *that's* abnormal.
2) Palpitations are when you can feel your heart beating. It's normal to become aware of it every now and then, and you'll probably notice that it only happens when something draws your attention to your heart.
3) When you feel your heart skip a beat, it feels like it's going to stop. You get a little lightheaded and that can easily scare you. But you can jump start your heart back into the normal routine by forcing yourself to make a good cough.
4) By all means take your pulse. Learn how your heart normally works. After weeks or months of normal operation, you'll realize that everything is okay and you'll also be confident that you can notice when something not normal happens. That feeling of control is key to getting through it.
5) When your heart beats fast, you feel faint, but you won't pass out. You only pass out when your heart beats too slowly, not when it beats too fast.
6) When your heart beats too slow and you feel faint, lie down so that the slower beats move more blood to your brain. This only happens to me when I hurt myself and the pain slows down my heart (your body does this to get you prone so that blood can circulate more easily).
I don't worry about my heart anymore, so it's possible to get through the fear. I hope that makes you guys feel better.