Is Allapostolic Teaching Infallible?

I'm not sure. I don't know that all apostolic teaching was infallible. Sometimes the apostles disagreed, sometimes they needed to be corrected by each other. But what I know is infallible is that which is given to us as the very words born of the Holy Spirit. No church can avoid schism without a Supreme Court. Therefore an authority must exist that is infallible outside of scripture.