The Torah prohibits, generally, the infliction of a wound on yourself or someone else. See Lev. 19:28. The obvious exception is the commandment to perform a bris millah (circumcision) on a male convert or eight-day-old Jewish male. But from where do we find a justification to pierce a girl's ear or nose? I know that, in Rivka, we have precedent for piercings, but how is that justified against the commandment?
Read Igros Moshe Choshen Mishpat 2:65 and 66 who discusses elective surgery and difference between destructive wounds and none harmful wounds.The tshuvah is very lengthy and goes through the gemara,Tosfos and Rambam.At the end of the tshuvah he brings a gemara in Bechoros 45a which brings a case of a person person who has an extra finger and then removes it ,it is called a mum(deformity) and since the Mishna doesn't say "even though it is incorrect" it is a bit of a proof that in a case of beautification it is allowed.Same would apply to a women that if it is for beautification it would be permissible.See the tshuva inside for the whole back and forth of the sugya. http://hebrewbooks.org/pdfpager.aspx?req=921&st=&pgnum=286&hilite=