“My Lord and my God!” -- John 20:28

Out of context, it seems like Thomas claims Jesus is his God.

Before we jump to conclusions we need to understand the background of Thomas.

Now Jesus loved Martha and her sister and Lazarus. So, when he heard that Lazarus was ill, he stayed two days longer in the place where he was.

Then after this he said to the disciples, “Let us go to Judea again.”
The disciples said to him, “Rabbi, the Jews were just now seeking to stone you, and are you going there again?”

...

So Thomas, called the Twin, said to his fellow disciples, “Let us also go, that we may die with him.”

John 11:5-8,16 (ESV)

At this point the disciples, especially Thomas did not believe Jesus was God or capable to defend himself against the Jews who were seeking his death.

Jesus answered: “...Let not your hearts be troubled. Believe in God; believe also in me. In my Father's house are many rooms. If it were not so, would I have told you that I go to prepare a place for you? And if I go and prepare a place for you, I will come again and will take you to myself, that where I am you may be also. And you know the way to where I am going.”
Thomas said to him, “Lord, we do not know where you are going. How can we know the way?”
Jesus said to him, “I am the way, and the truth, and the life. No one comes to the Father except through me. If you had known me, you would have known my Father also. From now on you do know Him and have seen Him.”

-- John 14:1-7 (ESV)

A few chapters later, despite being in Jesus presence, Thomas still challenged Jesus: "How can we know the way?" This Thomas said after witnessing how Jesus revived Lazarus from the dead (John 11:44).

Note that Jesus told Thomas that God is distinct from him in verse John 14:1 when he told Thomas to separately also believe him. Therefore, when Jesus said "you do know Him and have seen Him" Thomas should not have thought that means Jesus think he is God. However, this could possibly explain why he glorified God while speaking to Jesus.

Thomas likely also witnessed Jesus' crucifixion and death which would have confirmed his doubt.

Now Thomas, one of the Twelve, called the Twin, was not with them when Jesus came.

So the other disciples told him, “We have seen the Lord.”
But he said to them, “Unless I see in his hands the mark of the nails, and place my finger into the mark of the nails, and place my hand into his side, I will never believe.”

-- John 20:24-25 (ESV)

So when Jesus appeared 8 days later, Thomas was very surprised to realize he was wrong. Thomas addressed both his Lord (Jesus) and his (invisible) God.

When we look at the Greek it is much more likely that there are 2 referents in this verse

καὶ ἀπεκρίθη Ὁ Θωμᾶς καὶ εἶπεν αὐτῷ ὁ κύριός μου καὶ ὁ θεός μου

The Granville sharp rule states “When the copulative kai connects two nouns of the same case, [viz. nouns (either substantive or adjective, or participles) of personal description, respecting office, dignity, affinity, or connexion, and attributes, properties, or qualities, good or ill], if the article ho, or any of its cases, precedes the first of the said nouns or participles, and is not repeated before the second noun or participle, the latter always relates to the same person that is expressed or described by the first noun or participle”

We have ὁ (Ho)(the definitive article) followed by the noun κύριός (Kyrios) Lord followed by καὶ (and) then followed by another ὁ (Ho)(the definitive article) again followed by the noun θεός (Theos) God

Using the Granville sharp rule it is very clear in the Greek that Thomas has 2 referents and is NOT referring to Jesus as Both Lord of him and God of him. There are in fact 2 (Ho) definitive articles in this verse. One (Ho) preceding the first noun Kyrios which is in the Nominative masculine singular form and another (Ho) article before the second noun Theos which is also in the nominative masculine singular form. So Ho precedes the first noun but then IS repeated before the second noun.

The “rule” is not used within John 20:28.

Thomas was not calling Jesus God but declaring the recognition of Jesus as Lord and also of his God who had raised Jesus from the dead. There 2 separate referents in the statement by Thomas.

-- ljthriepland

If Thomas really worshipped Jesus as his God, then there should have been more records of the other disciples doing the same when Jesus appeared to them. (John 20:16, 20:19-20; 21:7-14)

If the author of the book of John, who recorded this event, believed Jesus is God, then this proclamation would have been a good opportunity to highlight that Jesus was after all God, yet only 3 verses further he wrote:

These are written so that you may believe that Jesus is the Christ, the Son of God, and that by believing you may have life in his name. -- John 20:31 (ESV)