It appears nose rings were just fashion at the time. Rebekah being offered one in Genesis by Abraham’s servant was just an offering and the nose ring itself wasn’t anything particularly significant.
Nose rings are mentioned in the Bible as far back as the book of Genesis. When Abraham sent his servant in search of a wife for Isaac, the servant prayed that God would reveal to him the right young woman (Genesis 24:12–14). Rebekah came in answer to his prayer, and when she agreed to give him lodging in her father’s home, he gave her some gifts from his master, Abraham. Among those gifts was “a gold nose ring” (Genesis 24:22). This reveals that nose rings were in fashion during that era and they represented wealth and status when given as gifts. They were also considered female attire. The only time men wore anything through their noses was when they were taken as slaves (2 Chronicles 33:10–11).
In Ezekiel 16, God describes the affection He had showered upon Israel in terms of a man showering his bride with gifts: “I put a ring on your nose, earrings on your ears and a beautiful crown on your head” (verse 12). The Lord often used figurative speech and familiar objects and customs in order to communicate unfamiliar truths to His people. The lavish adornment, including the nose ring, described in this passage was the way a wealthy, loving husband would have provided for his beloved.