Let us examine this verse given to Israel in light of of the New Testament doctrine of Justification by faith.
Exo 15:26 And said, If thou wilt diligently hearken to the voice of the LORD thy God, and wilt do that which is right in his sight, and wilt give ear to his commandments, and keep all his statutes, I will put none of these diseases upon thee, which I have brought upon the Egyptians: for I am the LORD that healeth thee.
Faith in Christ is greater than the law. No one can meet all the requirements of the law, although we should obey God from our hearts. Did Jesus heal by our law keeping or by his grace by faith? Did he heal some who came to him? or all who came to him? When he walked the earth he healed all who asked of him to be healed.
Mat 4:24 And his fame went throughout all Syria: and they brought unto him all sick people that were taken with divers diseases and torments, and those which were possessed with devils, and those which were lunatick, and those that had the palsy; and he healed them.
His healing was limited in places that did not believe in him.
Mat 13:57 And they were offended in him. But Jesus said unto them, A prophet is not without honour, save in his own country, and in his own house.
Mat 13:58 And he did not many mighty works there because of their unbelief.
The Gentile Roman Centurion believed in Jesus to just speak healing and he knew his servant would be healed.
Mat 8:9 For I am a man under authority, having soldiers under me: and I say to this man, Go, and he goeth; and to another, Come, and he cometh; and to my servant, Do this, and he doeth it.
Mat 8:10 When Jesus heard it, he marvelled, and said to them that followed, Verily I say unto you, I have not found so great faith, no, not in Israel.
So healing today is not as much about our law keeping as it is by faith in Jesus, our righteousness and our healer. We may pray for others in faith based on our righteous standing in Him. He will answer if we pray in faith and in his will.
Jas 5:16 Confess your faults one to another, and pray one for another, that ye may be healed. The effectual fervent prayer of a righteous man availeth much.
A righteous man is righteous by faith in Jesus. Our righteous faith in fervent prayer is aided by confessing our sins, forgiving others and seeking to do his will. What we cannot do, God is able to do through his grace. Be available to others saved and unsaved to pray for them. As we get to know them better we can also pray for their salvation. The only hindrance is no faith to ask for prayer.
Some are angered by "faith healers" thinking that a man is claiming to heal, when healing is from God. This title requires the gift of healing and it is by the Spirit of God. God is to be glorified, not a person.
1Co 12:9 To another faith by the same Spirit; to another the gifts of healing by the same Spirit;
God is to be glorified, not a person. Healing is of God by his grace through faith. Never are we to accuse another who is not healed, that they lack faith; this is hypocritical and wrong. The act of healing is the sovereign will of God, in his time in his choosing and for his purpose.