In what has so far been a futile attempt to improve my Spanish listening ability, I’ve been buying music from various Spanish-speaking countries. Belinda, a young Mexican, is one of these artists. In several of her songs, she uses phrases like “tu nombre está en mi piel,” or “la flora de tu piel,” or similar things with “piel.” Now, I can come up with plenty of metaphorical interpretations, but it got me wondering whether there was some common use of “piel” as a Mexican colloquialism, or whether she’s just exercising poetic license. Thanks.
Poetic license. The phrases you’ve mentioned, particularly “tu nombre esta en mi piel”, are used in other romantic songs/poems not restricted to Mexico. Belinda is a young pop artist who specializes in young romantic love songs… hence the use of those phrases. 
That phrase translates roughly as “your name is (tattooed) on my skin”…