Since there is no record of your baptism and no way to confirm that you were baptized, yes, you would need to be conditionally baptized. Because baptism is a one-time sacrament that can never be repeated, conditional baptism is a means of baptizing those whom it is not known whether they were baptized. You would be conditionally baptized upon your entrance into the Church and the formula would be stated “If you are not already baptized, I baptize you in the name of the Father, and of the Son, and of the Holy Spirit.”
