If you were baptized in the name of the Father, Son, and the Holy Spirit in a Trinitarian church, then there's no reason for you to do so. God's promises don't depend on us, but rather on Himself. What He gave you, what He promised you, and has done for you in your baptism is His work, His gift, His grace for you.
Instead, when you think on your baptism (whether you can remember it or not), be encouraged by the words of Scripture: Christ died for you, your sins are forgiven, the Holy Spirit lives in you, you are a new creation in Jesus Christ, you are born again by the grace of God, adopted as God's child and heir, united to Christ's death and resurrection. You have died to the world, and have been made alive with and in Christ, to God, that you might walk in faith and live by carrying your cross as the disciple of Jesus.
We don't get baptized as an outward symbol for the sake of ourselves, for the sake of others in the congregation, for pastors, or parents, or even for God. We are baptized because God has invited us to have life from Him. Consider what Paul writes in Titus 3:5, that it is not by works of righteousness we have done, but rather the washing of regeneration and the renewal of the Holy Spirit, God saves us by His mercy alone.
Thus baptism is God's seal and promise to you of what Christ has done, and what you have in Christ, that you might trust and believe, and be bold in your faith that God has saved you, is saying you, and will save you. That you are freely justified by His grace, apart from your own works, because of what Christ has already done for you, for me, and for every sinner.
To get "re-baptized" is, in a way, saying to God, "What you did for me isn't enough, I need to do something more". I know that isn't your intent, I know you don't mean it to be ill-intended. But it is important to know what baptism is and means, because we aren't baptized for God. Rather God baptizes us out of His love and grace. The human person who conducts the baptismal rite isn't the one baptizing you, it is God who is baptizing you. That is why baptism is God's work, not our own. And because it is God's work, we can be confident in what He has done and told us. Believing in His promises, and resting in His word.
Abide and be comforted in Him, who has given you Himself in your once-and-for-all baptism. For God placed His very Name in that water, to call you His own.
If you want a symbol of faith you can express, profess, there are many ways we can do that, every day of our lives. Through prayer, through singing our hymns, through icons, by reading and believing the Scriptures, by holding firm to what we confess in the Creeds. Every day is filled with opportunity to profess and confess our faith, we don't need to "redo" what God has already done to have that.
-CryptoLutheran