Sollozar means "to sob" or "to weep convulsively." It's a more intense and dramatic word than simply "llorar" (to cry), conveying a deeper level of emotional distress.
In the song, the lyric "Mi alma quiere sollozar" (My soul wants to sob) powerfully expresses the singer's profound sadness and inner turmoil. It highlights the struggle between his overwhelming grief and his pride, making it a memorable and emotionally charged word.
Diego Verdaguer's "Quién De Los Dos Será" is a passionate plea from someone on the verge of emotional collapse after a breakup. He's "a punto de estallar" [about to explode] and thinking only of her, his soul wanting to sob, but his pride holding him back. You can really feel his internal conflict here!
He's carrying a pain he has to endure because he didn't want to hold onto her, and now he's stuck wondering who will give in first. He sings, "No sé quién de los dos será quien se puede rendir al fin" [I don't know which of us two will be the one who can finally surrender]. It's a classic standoff, both too proud to make the first move, even though he admits, "Yo lo podría resolver" [I could solve it]. He's desperate for their love to return to its former glory, even as he's "triste sin ella" [sad without her] and the pain is killing him.