Is the Italian phrase 'Quando ti ho visto nell'aeroporto ho sentito completa per la prima volta in tre mesi Quando sono senza te mi manca un pezzo di mio cuore' correct?

Quando ti ho visto nell'aeroporto mi sono sentita completa per la prima volta in tre mesi; quando sono senza te mi manca un pezzo del mio cuore* is correct.

Specifically, the conjunction quando is "when." The personal pronoun ti means "(informal singular) you." The auxiliary ho and the masculine singular past participle visto mean "(I) have seen, saw." The word nell' means "in the" from the combination of the preposition in with the masculine singular definite article il ("the"). The masculine singular noun aeroporto means "airport." The reflexive pronoun mi, the auxiliary sono, the feminine singular past participle sentita, and the feminine singular adjective completa mean literally "(I) felt myself (to be) complete/whole." The preposition per means "for" in this context. The feminine singular definite article la means "the." The feminine singular cardinal adjective prima means "first (1st)." The feminine noun volta means "time." The number tre means "three (3)." The masculine plural noun mesi translates as "months."

The pronunciation will be "KWAN-do tee oh VEE-sto nel-LEYE-ro-POR-to mee SO-no sen-TEE-ta kom-PLEH-ta pehr la PREE-ma VOl-ta een trey MEY-sey" in Italian.

The present indicative sono is "(I) am" in this context. The preposition senza means "without." The emphatic personal pronoun te means "(informal singular) you." The personal pronoun mi means "(to) me" in this context. The present indicative manca literally means "(it) is lacking/missing." The masculine singular indefinite article un means "a, an." The masculine singular noun pezzo means "piece." The word del means "of the" from the combination of the preposition di ("of") with the masculine singular definite article il ("the"). The masculine possessive article mio means "my." The masculine noun cuore translates as "heart."

The pronunciation will be "KWAN-do SO-no SEN-tsa tey mee MAN-ka oon PET-tso dehl MEE-o KWO-rey" in Italian.

*There is nothing wrong with the phrase di mio cuore (pronounced "dee MEE-o KWO-rey"). It definitely may be more likely than del mio cuore in colloquial, conversational, informal or regional Italian. Italian puts in the equivalent of the definite article "the" where English does not. Italian language speakers will be more likely to drop them regarding phrases arising from the more personal relationships implicit in situations of "I, me, my" and "(informal singular/plural) "you, your, yours."