If I understood the question correctly, this is a question about the two differing descriptions applied to Christian baptism. Acts 2:38 talks about being baptised “in the name of Jesus Christ” whereas Matthew 28:19 talks about being baptised “in the name of the Father and of the Son and of the Holy Spirit”. The question then is, are these two different baptisms.
To answer this question we need to understand something of the meaning of the phrase “in the name of”. This expression may seem strange to modern English readers as it derives from a Hebrew/Aramaic idiom meaning “for the sake of”. When the New Testament writers talk about being baptised “in the name of”, they are not invoking some incantation or spell. It is simply a way of describing the reason and purpose of baptism.
One way of describing Christian baptism was “in the name of Jesus”, that is for the sake of Jesus. This distinguished Christian baptism from other types of baptism and ritual washing. Whereas you might be washed to become a Jewish proselyte or become ritually clean, only Christians were baptisms for the sake of Jesus.
Another way of describing Christian baptism was to describe the key elements of the Christian experience. Those are the relationship with God as a loving Father, the relationship with Jesus as God’s appointed heir, and the experience of the Holy Spirit through which the apostles were able to do amazing miracles. So Christian baptism could be described as being “in the name of the Father and of the Son and of the Holy Spirit”, capturing those three elements of the Christian experience.
The important point is that these are not two different forms of baptism but two different ways of describing the same baptism. So, in answer to the question, if when you were baptised and one form of words was used rather than the other you do not need to be re-baptised. The significance of baptism comes from its meaning as a symbol of new life, not from the form of words used.
See also: Is “in the name of the Father and of the Son and of the Holy Spirit” missing in early manuscripts?