There is no Vatican II document which "did away with" papal infallibility. Vatican II actually reaffirmed, in no uncertain terms, the teaching of Vatican I on papal authority.
The Dogmatic Constitution on the Church (Lumen Gentium) says this: "This teaching concerning the institution, the permanence, the nature and import of the sacred primacy of the Roman Pontiff and his infallible teaching office, the sacred synod proposes anew to be firmly believed by all the faithful" (LG 18).
The nun to whom you refer may have meant that Vatican II tried to finish what Vatican I began. Vatican I defined the role of the papacy in the Church but didn't get around to the episcopacy. As a result of the Italian invasion of the papal states and the Franco-Prussian war, Vatican I was unable to consider the place of the episcopacy in relation to the pope.
Vatican II restated Vatican I's teaching on the papacy, but also sketched out the role of bishops in the Church. Bishops as teachers and pastors acting in union with the pope are said to be acting according to the principle of collegiality.
There is a renewed stress on the pope as head of a college of bishops, but there is nothing which subordinates the pope to this college. In no sense can Vatican II be taken as "doing away with" papal authority as previously defined.