Does the water mentioned in John 3:5 refer to the water of baptism, or can it mean amniotic fluid?

Yes, they are. This is one of the passages in Scripture the exact meaning of which has been infallibly defined by the Church. The word “water” cannot refer to amniotic fluid or anything other than natural water, and the passage must be understood as referring to baptism.

The Council of Trent defined, “If anyone shall say that real and natural water is not necessary for baptism, and on that account those words of our Lord Jesus Christ, ‘Unless a man be born again of water and the Holy Spirit’ [John 3:5], are distorted into some sort of metaphor, let him be anathema” (Canons on the Sacrament of Baptism, 2). The footnote in the Living Bible for Catholics is out of sync with the magisterium in suggesting that any interpretation other than baptism is possible for a Catholic.