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You could check the Ironic Nursery Tune and Creepy Children Singing pages and see if anything rings a bell.
Thanks, I'll check it out.
UPDATE: Didn't find it, unfortunately, so would still be gratefull if anyone has any suggestions as to what it could be. :)
Edited by WhatWasIt
Sorry to suggest another trope page instead of the answer, as it doesn't sound familiar, but you could try the "Man on Fire" trope page. Hope you find it!
This was either a film or an episode of a TV series but I distinctly remember a man walking around a hospital or something, and he kept hearing a little girl singing a creepy version of the Hush Little Baby nursery rhyme. By the end of fhe film/episode, the man tried to set himself on fire and I can't remember whether he was successful or not . . . I know this isn't much to go on at all, but if anybody has any wuggestions and nos to what it might be I would be very thankful.