Jesus is called the Son of God  because of His nature.  He is the Son in the Trinity.  Just like a man can be a husband, a father, or a brother.   But He proved that He is God, by His actions.  His birth and death were prophesied in the Old Testament.   He said "If you have seen me, you have see the Father" (John 14: 8-11).   The leaders of the temple wanted to put Him to death because He claimed who He was.  He healed the sick, the lame and the blind, as it was predicted in the Old Testament. In Isiah 9:6 talks about the coming Messiah will be called the Son of God. The Trinity existed before the world was created.  So, Yes, He is both Son of God and God in flesh (John 1:1,  Gal 4:4)