Inaccuracies on the term "prince"

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I'm not sure he was a prince, because his father, Zhao Tuo (Trieu Da) was a commander or general of a Qin expeditionary force at the time they arrived at the kingdom of Au Lac in North Vietnam. It is ONLY after the fall of Au Lac did Zhao Tuo establish the kingdom of Nanyue (Nam Viet). But, according to the legends, Trong Thuy has already committed suicide. Even if he was prince, it would be a posthumous title, but there's no source that can verify this he received a posthumous title.