Hi Worker Bee,
Welcome to Healing Well! I've never heard a question about swimming, but it's possible that many here have experience with it. I can say this. You could be getting pain symptoms in your esophagus due to the stretching and movement required by swimming aggressively. Your esophagus interprets all pain the same way, so any pain you're experiencing will feel exactly like heartburn.
I know that those of us who have had this surgery will develop adhesions that may pull when stretched. Also, it just may create some pull on the wrap itself. That said, just because it's bothering you now, doesn't mean it will always bother you. I have noticed that past the year mark I was still getting better.
Maybe you could try some different strokes and see if one of those might not cause the same pain. I'm no doctor, but it sure sounds as if you're pulling on something and it's causing you pain. Any pain in the esophagus leads it to send the "heartburn" message to the brain.
Happy Swimming! You might have to take it a little slower and see if you can find something that works for you.