Let's separate out the different issues:
Is it wrong to say that Jesus is the God of the Old Testament?
No, it is correct to refer to Jesus as the God of the Old Testament, just as it is right to refer to the Father and Spirit as the God of the Old Testament. One instance of this can be seen in Isaiah 6 where Isaiah sees Yahweh, and in John chapter 12, John references this passage and says it refers to Jesus (John 12:41):
Isaiah said these things because he saw his glory and spoke of him.
From this text, many Christian theologians believe that the theophanies of the Old Testament (theophanies are instances where God appears) are in fact Jesus, and not the Father or the Spirit.
Now to the next issue:
From what I understand, Jesus existed eternally correct? And Jesus is God and didn't come into being when he was sent on Earth.
Yes, Jesus eternally exists as God (see John 1:1). However, He did not take upon Himself a human nature until His incarnation. For a fuller treatment of this subject (the pre-existence of Jesus), see the book "The Forgotten Trinity" by Dr. James White.
There was a group called the marcionites that argued that there are 2 Gods because the God of the OT and the NT are just too different like
Yep, they did argue that. But the Christian church argued back vociferously, pointing out that God is consistent in both the Old Testament and the New Testament. In both the Old and New Testaments, for example, God is seen to be making judgement against sin (in the judgements in the Old Testament, and the book of Revelation), and also showing mercy and grace (seen in the book of Jonah most clearly in the Old Testament and in the clear proclamation of the forgiveness of sins in the New).