Yes, I will try to calm you down. My son went through this at age 3. He had had a heart murmur for quite some time, but no one referred us for follow-up until he was 3. Most heart murmurs are "innocent," but they just like to make sure. In the rare case they do find a problem, they are correctible by surgery (unlikely and scary, but surgeons can do a lot). The most difficult part of the EKG for us was having our son be completely still for the procedure. However, the pediatric cardiologist and his assistants were SOO good at this. I can't believe how well it went. The EKG confirmed for us that our son had an "innocent" heart murmur. He is 15 and still has it. I have to note it on his medical records and I periodically get asked about if he sees a new provider, but all I have to say is that it's been checked.
What to expect--cardiologists can often just listen to a heart murmur and tell if it's innocent. Sometimes they follow up with the EKG just to be sure, which is what happened in our case. We met with the doctor, they did the EKG and we were happily on our way. I can't remember what tactics they used, but my son was a VERY active 3-year-old and they did a good job getting him to be still.
Ironically, he had a preschool classmate going through the same thing at the same time. Hers was not innocent and she had to have major surgery, but it was a complete success and she was back in preschool a few weeks later from what I recall.
Good luck--chances are you doctor is right that it's no big deal and they are just being cautious. Innocent heart murmurs are very common. If your doctor isn't overly concerned she probably thinks it sounds innocent upon listening, but just wants to verify that.