First of all, I'd say that most people know for sure if a story they tell is true or not. (If they honestly don't know, then it falls into the realm of the personal equivalent of an urban legend, a fable, or simply a speculative memory.)
Your story is technically a lie (it's not truthful—or at least not entirely truthful), but it's being said in order to enhance something for dramatic effect rather than to mislead per se.
In that sense, it's more like an embellishment.
From the Merriam-Webster thesaurus entry:
2 the representation of something in terms that go beyond the facts
// the actorʼs penchant for embellishment suggests that his memoirs would be more appropriately shelved in the fiction section
Synonyms of embellishment
caricature, coloring, elaboration, embroidering, embroidery, exaggeration, hyperbole, magnification, overstatement, padding, stretching
Words Related to embellishment