Though it is true that in the Old Testament this oil was used, but in the New Testament Jesus healed by the power of the Holy Spirit. Also the peoples faith healed them as well.

"And He said to her, Daughter, your faith (your [Joseph Thayer, A Greek-English Lexicon.] trust and confidence in Me, springing from faith in God) has restored you to health. Mark 5:34

And Jesus said to him, Receive your sight! Your faith ( [Joseph Thayer, A Greek-English Lexicon.] your trust and confidence that spring from your faith in God) has healed you. Luke 18:42


If i'm wrong feel free to correct me