I'd be very surprised if you 'grow out of it.' I started getting mild symptoms around the time that I hit puberty, and it got progressively worse until I had the ablation at 22. Also, my understanding is that arrhythmias often get worse during pregnancy and can endanger the life of the mother and baby (not to mention that you may or may not be able to continue taking any medications during that time). I know you're too young to be thinking of having kids anytime soon, but it's something to keep in mind!
If your insurance won't cover it, I can see why your parents would rather wait it out. I strongly suspected I would need this done when I got my first job out of college and got the best insurance my employer offered based on that assumption. I only had to pay the $20 co-pay for the electrophysiologist, but I will always remember seeing the insurance statement showing what they paid out- it was about $65k.