I disagree. It's made up because some protestants cannot understand the role of Baptism with water.
In Acts1:5 Luke writes that Jesus told the apostles
"for John baptized with water, but before many days you shall be baptized with the Holy Spirit.”
In his gospel Luke writes that Jesus told the apostles
"And behold, I send the promise of my Father upon you; but stay in the city, until you are clothed with power from on high.” (Lk 24:49)
I believe both are referring to the coming of the Holy Spirit at Pentecost.
But we don't people going on about anything about "power clothes".
"Have you got your power clothes yet?"
It's obviously a metaphor, the same as Acts 1:5
This is because you are defining the word by its strictly religious meaning in modern times rather than interpreting the Greek word according to its base meaning of "immerse." It was not a strictly "religious" word during New Testament times and thus did not carry a strictly "religious" meaning. The analogy of being "clothed in power" is indeed a metaphor, but βαπτίζω was used in Greek of immersing bread in wine, of cities being immersed in people (i.e. becoming crowded), of ships becoming immersed in water (i.e. sinking), and of people being immersed in water when they were simply bathing (not undergoing a purely religious ritual).
This is how you understand the accurate meaning of the word. When Pentecost came, they were immersed in the power of the Holy Spirit just as when they were immersed in water in baptism. Both were "baptisms" in two different substances; one water, the other the Holy Spirit and Fire.
Scripture doesn't use the term "Baptism with the Holy Spirit" only the verb form.
It's not a metaphor, unless one thinks that every time they dipped bread in wine they used a religious metaphor to describe how they were "baptizing" it, and if it the verb form is not a metaphor then your argument falls flat. It is proper to use the term baptism in water because they were being baptized in water, and it is proper to use the term baptism in the Holy Spirit (whether the noun form actually appears in scripture or not) because they were being "baptized," i.e. immersed in the Holy Spirit.