You were taught incorrectly.
Can. 11 Merely ecclesiastical laws bind those who have been baptized in the Catholic Church or received into it, possess the efficient use of reason, and, unless the law expressly provides otherwise, have completed seven years of age.
Can. 12 §1. Universal laws bind everywhere all those for whom they were issued.
Can. 204 §1. The Christian faithful are those who, inasmuch as they have been incorporated in Christ through baptism, have been constituted as the people of God.
§2. This Church, constituted and organized in this world as a society, subsists in the Catholic Church governed by the successor of Peter and the bishops in communion with him.
Can. 205 Those baptized are fully in the communion of the Catholic Church on this earth who are joined with Christ in its visible structure
Can. 879 The sacrament of confirmation strengthens the baptized and obliges them more firmly to be witnesses of Christ by word and deed and to spread and defend the faith.
You are correct that the Eucharist and Confirmation strengthen our bond with Christ and complete the Sacraments of Initiation.
You are not correct that until one receives these other two sacraments a person is not fully Catholic. Catholics, by virtue of our Catholic baptism, are bound by Canon Law. For those baptized in non-Catholic communities, they become Catholic when they make their profession of faith. They OP was baptized Catholic. Therefore, the OP is a Catholic for matters of completion of their other Sacraments. They are not the same as a candidate or catechumen.