The Father is called God the Father several times in the Bible. But the Son is never called God the Son. So we have no right to call him God the Son. He might be God, but we cannot be sure, the Bible does not make it clear, we are not supposed to know.
Also I disagree that the Father and the Son have equal authority over the creation. They are not equal, and the Son's authority comes from the Father. For example John 5:27 says the Father gave the Son the power to judge. Or in John 8:28, Jesus says "... I do nothing on my own, but I say only what the Father taught me".
In fact, the Son is part of the Father's creation. Read Rev. 3:14 in KJV for example "And unto the angel of the church of the Laodiceans write: These things saith the Amen, the faithful and true witness, the beginning of the creation of God." Similarly in Col. 1:15 "... the firstborn of all creation". Most Christians claim Jesus always existed, but there is no verse saying that, or saying he was not created. Rev. 3:14 and Col. 1:15 say he was created. So when the Father has authority over all creation, he has authority over Jesus too.