It's no surprise that heartburn is aggravated by soda. Most soda contains phosphoric acid. It's very acidic. Our bodies try to maintain a neutral blood pH, so calcium may be pulled from the bones to neutralize the acidity.
High Consumption of Soft Drinks Is Associated with an Increased Risk of Fracture: A 7-Year Follow-Up Study - PMC

I've seen this chemical in the ingredients list of ice tea, as well.

If you really need to have a "fizzy drink," add some 100% fruit juice to seltzer, which is just water with carbon dioxide added for the fizz.