It wasn't a
heart attack, you'd KNOW if it was a heart attack. Even if you had one and survived, the EKG would have shown abnormalities. Plus, I notice you didn't mention anything about pain, and pain is one of the most common symptoms of a heart attack.
Trust the EKG. EKGs are an invaluable tool in the medical world. They check and test the machines daily in hospitals to make sure they are in proper working order more then one person reads your EKG, just to be sure. To be honest, I have never heard anyone say they are inaccurate before...
I'm going to throw a few guesses out here, to give you some other ideas to look into:
It could be
Angina, which is
chest pain caused by a lack of blood to the heart. Angina is a minor problem (I know it sounds major), and in some cases, all it takes it a few deep breaths to get proper perfusion. Angina is commonly known for just "going away" after breathing deeply and relaxing.
As you said, you may just have panic attacks. Maybe you should talk to your personal doctor about it, see if some kind of medication can help curb these symptoms (of course, being so infrequent, he may just tell you to not worry)
As for the 3 that happened at night... if it happened in the middle of the night, it could be
sleep apnea, or, even less, you just have really intense
nightmares, and don't remember them.
Well, thats my 2 cents. I hope it at least gives you some good places to look. Good luck on your search for a diagnoses!