If you refer to Psalm 22:1 (NLT) and compare that with Matthew 27:45 (NLT), you will see that the wording from the Hebrew language is identical.
King David prophesyed Psalm 22 (NLT) 1000 years before the Crucifixion of Christ right down to the Roman soldiers casting lots for Christ's clothing. Again, compare Psalm 22:18 (NLT) with Matthew 27:35 (NLT) and you will also see that the wording from Hebrew is identical.
Nowhere in God's Word does Christ ever refer to God as God... Christ ALWAYS refered to God as "Father".... except as quoted in Matthew 27:35 (NLT).
When Christ said, "My God, My God, why hast thou forsaken me?" - Christ was not calling out to God in acclaimation. He was TEACHING from the cross to His very last breath in quoting King David's 22nd Psalm and letting everyone know, who witnessed his impending death, that in fact, He WAS the Messiah. Christ knew that his mission was to sacrifice Himself for us all. He was not distraught at His own death - far from it... it was what He was placed on earth in a flesh body to ultimately do for everyone. He knew that the death of the flesh is not something to be terrified of - in fact, he was just taking a short trip back to Heaven to carry on with things. After His resurrection, He even met up with some of his followers on the road to Emmaus as found in Luke 24:13-53 (NLT) and told them not to worry for He was still with them.
I hope that assists you in your understanding of those passages as taken from the original Hebrew language.