Acts 5:12-16

At the hands of the apostles many signs and wonders were taking place among the people; and they were all with one accord in Solomon’s portico. 13 But none of the rest dared to associate with them; however, the people held them in high esteem. 14 And all the more believers in the Lord, multitudes of men and women, were constantly added to their number,  15 to such an extent that they even carried the sick out into the streets and laid them on cots and pallets, so that when Peter came by at least his shadow might fall on any one of them. 16 Also the people from the cities in the vicinity of Jerusalem were coming together, bringing people who were sick or afflicted with unclean spirits, and they were all being healed.

After the death of Anania and Sapphira, great fear came over the church (v. 11). Then also, because of the great miraculous power of healings and casting out demons by the Apostles—especially by Peter—the people dared not associate with them.

This power was given to all that believed after the Holy Spirit came at Pentecost. I would say that it was given to some more than others, according to their faith. It seemed to be especially given to Peter (v. 15). He, and I suppose some of the other Apostles, had the same healing power that Jesus had; for “they were all being healed” (Mk. 16:17-18; Lu. 24:49).