According to a number of scriptures it seems that the following doctrinal conclusions can be drawn:
(1) It is proper to wear earrings
(2) It is proper to wear nose rings
(3) The type of earring and nose rings worn at that time cannot be determined from the text.
But it is unlikely that the servant of Genesis 24 put holes in Rebekah ear or nose when he gave her the jewlery. But then perhaps she already had holes in her ears and/or nose.
See Of the Bible for an analysis of scriptures related to nose rings and earrings.