Jesus has shown how a shepherd can do and should do. In His life on earth He has shown us what God (the Father in heaven) is like and what are on the heart of God. Jesus’ ministry is a healing ministry. His healing brings wholeness. He came to give this wholeness, abundant life. (John 10:10) Jesus expects His believers to do the same as He did and even greater because He has given us His Holy Spirit. (John 14:12-14)
Here are verses from Matthew recording that Jesus healed al the sick brought to Him. He never rejected anyone.
News about him spread as far as Syria, and people soon began bringing to him all who were sick. And whatever their sickness or disease, or if they were demon possessed or epileptic or paralyzed—he healed them all.
That evening many demon-possessed people were brought to Jesus. He cast out the evil spirits with a simple command, and he healed all the sick.
[ Jesus, God’s Chosen Servant ] But Jesus knew what they were planning. So he left that area, and many people followed him. He healed all the sick among them,
Jesus saw the huge crowd as he stepped from the boat, and he had compassion on them and healed their sick.
When the people recognized Jesus, the news of his arrival spread quickly throughout the whole area, and soon people were bringing all their sick to be healed.
They begged him to let the sick touch at least the fringe of his robe, and all who touched him were healed.
Large crowds followed him there, and he healed their sick.
~~~~~~~~~~~~~~~~~~~~~~a word of warning:
In the following message prophet Ezekiel received from the Holy Spirit, God took note of and reprimanded the spiritual shepherds (the religious leaders then) who did not heal their sheep!
Shepherds (religious leaders, equivalent to the pastors today) are required and expected to heal the sick sheep (congregation, church members). It means they can do it but they do not want to do the healing.
God is still watching and taking note of this attitude of the heart. God is not talking about doctors. God is talking about pastors or ministers or whatever their religious titles may be, whether they qualify. Healing the sick is on their job specification.
Ezekiel 34:3-5 New King James Version (NKJV)
3 You eat the fat and clothe yourselves with the wool; you slaughter the fatlings, but you do not feed the flock. 4 The weak you have not strengthened, nor have you healed those who were sick, nor bound up the broken, nor brought back what was driven away, nor sought what was lost; but with force and cruelty you have ruled them. 5 So they were scattered because there was no shepherd; and they became food for all the beasts of the field when they were scattered.