Some people have this problem even when they don't have any reason to fear heart problems -- it's because for some people the labored breathing of exercise makes them feel similar to when they're having an anxiety attack. It's just a conditioned response -- you'll get past it.
The best way to get rid of your anxiety is taking medication, therapy and healthy lifestyle. In health anxiety, our mind always make us believe like this but its all in our mind.
Best way to stop those horrible feelings is ignoring it, make your self busy, talk to others and do some hobbies.
I'm not a doc but I know a little about SVT and have experienced it myself on several occasions. It can be scary, for sure. SVT is a fairly common thing with young adults, and generally resolves itself within a few minutes. There are some strategies for snapping out of it, like doing a vagal maneuver or splashing ice cold water on your face. From what I understand, it typically comes on at random and not necessarily the result of exercise. So if you're concerned about exercise bringing about SVT, I think that fear is unfounded. Your heart likes to beat, and it even likes to beat hard and fast sometimes. It's good for it. Think of your heart as a sports car -- it would be a darned shame if you only drove it less than 30 MPH. Rather, you want to take it out on the open road and get it going 80 or 90 sometimes! Your heart's the same way. A sports car WANTS to go fast. So does your heart. Don't deny it the fun of a good workout! I hope that helps. One last thing -- don't get another ablation without a second or even third opinion from other cardiologists.