It was the most gut-retching thing I have ever heard.
Wrenching sounds like it would make sense, but so does retching.
I think you want "gut-wrenching"; "retching" involves something coming up from your gut and out of your mouth: also called puking or throwing up, although normally retching refers to the sound and motion of throwing up with or without any actual regurgitation.
Something that is gut-wrenching is extremely disconcerting in a visceral sort of way. You might throw up as a reaction but that is not the usual outcome, and certainly it's not a necessary condition.