Is it wrong to say Jesus is the God of the Old Testament?

It is not wrong to say what you genuinely believe regarding the Old Testament, providing it does not conflict with the teachings of the Catholic Church. An element of the question is:

Jesus is God, the Father is God, and the Holy spirit is God.
With this is mind, is it wrong to say Jesus is the God of the Old Testament?

According to Christian belief, Jesus, the Father and the Holy Spirit are one, which means that at one level, all three are the God of the Old Testament. However, we are also shown that Jesus can speak and act independently of the Father, even praying to the Father (eg Mark 14:35). Likewise, the Father acts independently of the Son (and the Holy Spirit likewise).

There is nothing in either the Old Testament or the New Testament that demonstrates that any reference to God in the Old Testament ought to be read as referring to Jesus rather than to the Father. Some believe that when God appears in the likeness of a man (eg Genesis 3:8ff), that this must be Jesus, since the Bible says elsewhere that no one can look at God's face and live. However, these differences are readily explained by differences of authorship, with Genesis chapter 3 widely attributed to the 'Yahwist', a source for whom God was anthropomorphic. The Catholic Church (and most other Christian denominations) teaches that Jesus is only prophesied or foreshadowed in the Old Testament, and that it is the Father about whom we read in the first part of the Christian Bible.

Returning to the question:

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...

Marcion (85-160 CE) not only knew nothing of the Holy Trinity, he believed that God the Father could not have been the Creator God of the Old Testament, whom he called the Demiurge. The Catholic Church excommunicated Marcion because of his teachings, so clearly they should be regarded by Catholics as entirely wrong.

It is not wrong to say that Jesus is the God of the Old Testament because the New Testament shows that Jesus is active in the Old Testament times.

Jesus was the Rock.

1 Corinthians 10:3-4 (NASB)

3 and all ate the same spiritual food; 4 and all drank the same spiritual drink, for they were drinking from a spiritual rock which followed them; and the rock was Christ.

Jesus was the God whom Israelite people had tempted.

1 Corinthians 10:9 (NIV)

9 We should not test Christ,as some of them did—and were killed by snakes.

Jesus was the God of the Shema.

1 Corinthians 8:6 (HCSB)

6 yet for us there is one God, the Father. All things are from Him, and we exist for Him. And there is one Lord, Jesus Christ. All things are through Him, and we exist through Him.

Jesus was the God who saved a people out of Egypt.

Jude 1:5 (ESV)

5 Now I want to remind you, although you once fully knew it, that Jesus, who saved a people out of the land of Egypt, afterward destroyed those who did not believe.

Jesus was the God who chained fallen angels to Tartarus.

Jude 1:5-6 (ESV)

5 Now I want to remind you, although you once fully knew it, that Jesus, who saved a people out of the land of Egypt, afterward destroyed those who did not believe. 6 And the angels who did not stay within their own position of authority, but left their proper dwelling, he has kept in eternal chains under gloomy darkness until the judgment of the great day—

This is a reality because Jesus is a member of the Trinity.

Matthew 28:19 (NASB)

"Go therefore and make disciples of all the nations, baptizing them in the name of the Father and the Son and the Holy Spirit,

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.

And next:

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).