Is There a Supremacy or Infallibility in the New Testament?

There's no events of the new testament that depict supremacy or infallibility invested in peter specifically. In acts 15, thereis a doctrinal controversy. The apostles come together with presbyters of the church of jerusalem. But you never have anything that singles out peterasas though he's supreme. And these efforts to derive the dogma from the text are post hack. They're reading something back in. Itd be just like if, in second corinthians 11 28, paul says that he has a care for all the churches. If there's a supreme and infallible head of the church, it'd be pretty important to see that. Think how different that is