Religious sisters do not normally wear earrings because they are called to live a much simpler form of life. The simplicity of their lifestyle is a sign of their vocation in life. However what is specifically allowed or prohibited would be based on the particular rule of life for the religious order.
In Catholicism, wearing of jewelry is considered morally neutral. What affects the morality of the jewelry is what message the individual wearing them is trying to send and if one's health is affected.
Any Old Testament passage would not affect Christians since we are not bound to Jewish ceremonial laws. And New Testament passages that appear to be against jewelry are generally considered to fall under advice of the era for Christians to avoid shows of opulence but are not actual commandments against all jewelry.