Holly,
The support for the Trinity is derived primarily from Jesusā self-revelatory statements where he declares āthe Father and I are oneā and āthe Spirit and I are oneā. If the hearer believes what he/she hears then simple reasoning provides the rest; if A = B and B = C, then A = C. So the one nature of God is triune. Three in one is a mystery to be sure, but it is based on Jesusā own statements about himself. Another, āIf you have seen the Father you have seen meā¦ā
Concerning your reference to the command to baptize, Jesus commands the Apostles to baptize in His name, and His name (or identity ) is Father, Son and Holy Spirit.
The word āTrinityā does not occur in scripture, it came about later as the Church wrestled with all the ideas circulating about who or what is Jesus.
Also, I think your friend is claiming that this verse was not part of the original Gospel and was later āinsertedā as the belief in the Trinity developed in the church. This is a ātampered textā approach aimed at diminishing the credibility of the verse. I personally reject that idea concerning this particular verse.
PeterK