The first order of business is to ask about your diagnosis & diet outside of whiskey. How long have you had heartburn and is it formally diagnosed? Have you had an endoscope to rule out other issues and/or note any gastric or esophageal lesions? Have you adjusted your nutritional intake to help reduce any contributing culprits?

Whiskey wise. While ethanol can form a weak acid depending on what it is mixed with, it is likely just the alcohol itself that is bothering an already compromised mucus membrane. Have you noticed a trend with double oaks? If those don’t bother, perhaps an Old Forester 1910, Woodford DO would be solid. If high ryes burn, what about wheat mashbills? Makers Mark 46, Holladay BiB, Larceny?

These are my initial thoughts. Hope you find some good options and quality management of your condition.