I know where Christ instituted Baptism, Eucharist, and Confession. But what about the others?
From Scripture with regard to Confirmation:
Acts 8:14-17 - the people of Samaria were baptized in Christ, but did not receive the fullness of the Spirit until they were confirmed by the elders. Confirmation is a sacrament that Jesus Christ instituted within His Catholic Church to further strengthen those who have reached adulthood.
Acts 19:5-6 - the people of Ephesus were baptized in Christ, but Paul laid hands on them to seal them with the Holy Spirit. This sealing refers to the sacrament of confirmation.
Eph. 1:13 - Paul writes that the baptized Ephesians were sealed with the promised Holy Spirit, in reference to confirmation.
Eph. 4:30 - Paul says the Ephesians were sealed in the Holy Spirit of God, in reference to the sealing of confirmation.
Heb. 6:2 - Paul gives instruction to the Hebrews about the laying on of hands, in reference to confirmation, not ordination. The early Church laid hands upon the confirmand to administer the sacrament of confirmation.
Heb. 6:2 - this verse also refers to the cycle of life and its relationship to the sacraments - baptism, confirmation, death and judgment - which apply to all people.
John 6:27 - Jesus says the Father has set His seal on Him. As the Father sets His seal on Jesus, so Jesus sets His seal on us on the sacrament of baptism, and later, in the sacrament of confirmation.
From Scripture with regard to the Sacrament of the Sick:
Mark 6:13 - the apostles anointed the sick with oil and cured them. This is a sacrament of the Catholic Church instituted by Christ which heals us physically and spiritually.
James 5:14 - the presbyters (priests) are called to anoint the sick with oil and pray over them. Their sins are forgiven. This is the sacrament of the sick, also called extreme unction.
James 5:15 - during the sacrament of the sick, the priest’s prayer of faith will “save” the sick man, and the Lord will raise him up. The word “save” comes from the Greek word “sozein” which means an eschatological saving of life from death.
James 5:14 -15 - these verses demonstrate another example of how priests effect the forgiveness of sins (here, even without confession) by the power of Jesus Christ. Protestants have no plausible exegesis of this passage other than to acknowledge the sacrament of the sick.
Gal. 4:13-14; 2 Tim. 4:20 - Paul was afflicted with sickness. These verses show that not all illnesses were cured in the apostolic age.