With the correction made by Rusty, both sentences are OK, because there is the verb creérsela, which includes lexicalized pronouns, with that meaning of having fantasies, or delusional thoughts, or merely half cooked convictions of being something or having some qualities or merits that aren't there.
Le dijeron que cantaba muy bien [como elogio amable o simple cortesía] y se la creyó. Ahora está buscando empezar una carrera en la industria de la música. [and whoever told that is not the flattering culprit but the people who build themselves a castle using just one pebble]
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[gone]
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