I don't really know. It could be a true story with some artistic liberties taken, or it could be made up from start to finish. Without more information, it's difficult to tell.
I don't think 'American Nightmare' is a true story. Usually, works with such names are fictional works of imagination, crafted to engage and thrill the audience through fictional scenarios and characters.
Nightmare Alley is not based on real events. It's a work of imagination by the author to captivate the audience with a thrilling and fictional narrative.
It's most probably not a true story. Usually, such titles suggest fictional elements and are crafted for entertainment rather than being based on real events.