Acid-suppressing medication doesn't help, but low-dose tricyclic antidepressants seem to modulate the pain in some patients.

WSJ: Why Your Heartburn Drugs Don't Work

Early studies suggested a risk of limb malformation with tricyclic antidepressants, but the risk hasn't been confirmed by more-recent studies.

CNN: Antidepressants: Safe during pregnancy?

They found a small but significantly longer QT interval for SSRIs citalopram and escitalopram as well as for methadone and the tricyclic antidepressant amitriptyline.

FORBES: Popular Antidepressants May Put Patients At Risk For Serious Arrhythmias