Those who were given the power to heal and who were healing many, of course, just like the woman had faith that she would be healed if she could just touch Jesus' robe. That does not justify the invention of a whole new priesthood.That is your belief. Take a look in Acts. Whose shadow did the people want to fall over those who were ailing?
Now, if you use this to justify the Catholic priesthood, why are not Catholic priests known for mass healing like the Apostles were known? They have, according to you, the power to compel Jesus to submit His body and blood for sacrifice again as well as forgive or withhold forgiveness of sin. Jesus Himself made the case that the power to forgive sin was greater than the power to heal, then proceeded to demonstrate that He had both the greater and lesser power, yet we're supposed to accept that priests have the greater power and not the lesser?