Is any one of you in trouble? He should pray. Is anyone happy? Let him sing songs of praise.
 Is any one of you sick? He should call the elders of the church to pray over him and anoint him with oil in the name of the Lord.  And the prayer offered in faith will make the sick person well; the Lord will raise him up. If he has sinned, he will be forgiven.  Therefore confess your sins to each other and pray for each other so that you may be healed. The prayer of a righteous man is powerful and effective.
 Elijah was a man just like us. He prayed earnestly that it would not rain, and it did not rain on the land for three and a half years.  Again he prayed, and the heavens gave rain, and the earth produced its crops. (James 5:13-18)
You asked, “Would James 5:13-18 be considered a congregational ministry or simply the confession and forgiveness of private individuals to each other?” As usual, pay attention to the context of the passage. Verse 13 refers to how one relates to God, not to other believers. Verse 14 sharply turns the focus to healing and continues all the way to verse 16. Then verses 17 and 18 follow the same vein in referring to miracles, expanding the topic to miracles of nature and miraculous answers to prayer in general.
Therefore, the topic is miracle healing, not confession and forgiveness among people. Miracle healing comes in several ways, and this passage refers to one way, that is, when the sick asks for prayer from church elders (v. 14) and other believers (v. 16). Verse 15 says that if this sick person has sinned, he will be forgiven. Verse 16 says to confess your sins “so that you may be healed.” This is the only reason the confession of sins is introduced. James is talking about the confession of sins only when a person’s sins are related to his desire for healing. If he has committed no sin related to his sickness, then confession does not apply.
Verse 16 describes a situation that would arise sometimes, but far from always. A person might come and ask me to pray for his healing. In the course of our discussion, he might finally admit, “I confess that I have dabbled in the occult, and I think this has something to do with my sickness, or it has been hindering me from obtaining healing. Now I admit that I have sinned, and I renounce the occult.” His sin might be adultery, or bitterness, or something else. He confesses his sin before me, but not because he has wronged me, and not because I am the one who forgives him. No, he confesses his sin before me because this happens in the context of his seeking healing from God by faith with my prayer and counsel. After this, I can pray for him and we can have the confidence that God forgives him and heals him.
Then, notice again that verses 17 and 18 continue to talk about miracles, not confession and forgiveness, expanding the topic to include even miracles of nature. Thus the passage is misused unless it is used to teach that all members of the congregation should request miracles, dispense miracles, and experience miracles, especially miracles of healing. It is a gross degradation and perversion of Scripture to use the text as a basis for some congregational ministry or event where the members confess their sins and forgive one another. Compared to the actual purpose, it would be a lame and grotesque use of the text. As long as there is no expectation and demonstration of miracle healing — such as cancers disappearing, cripples coming out of wheelchairs — the church defies the command of Christ.