Anxiety can definitely cause heartburn. When your anxious your body produces more stomach acid. I take Prilosec and it helps. Sometimes you can get chest burns with anxiety that aren't even related to heartburn. I hate those.
You can still have anxiety even when you feel calm. I know anxiety impacts our stomachs and digestive tracts, but not sure it causes heartburn. Have you tried things like Tums to help with the heart burn? Have you addressed this with your doctor? You truly need to "accept" that your heart is fine. I know it's hard to do this, but this constant worry and fear is fueling your anxiety and keeping it going strong. Heartburn is easily treated, you should see your doctor regarding this, and for peace of mind. Take care.