In the following verse, the only “modifier” I see Thomas using to qualify Jesus as “God” (the Son) is the possessive pronoun “my”:
Thomas said to him [Jesus], “My Lord and my God [ὁ θεός μου] !”
So, are you saying Thomas was mistaken in addressing Jesus of Nazareth as his “God”–on philosophical grounds (since you don’t believe Jesus is the Second Person of an eternal divine Trinity)? Or, are you saying that Thomas’s use of the possessive pronoun “my” with “God,” in reference to Jesus of Nazareth, somehow negates “God” meaning “God”—on grammatical grounds?
We see the same possessive pronoun “my” similarly used with “God,” this time in reference to God (the Father), here:
And my God [ὁ θεός μου] will meet all your needs according to the riches of his glory in Christ Jesus.
Further, if you do believe Thomas was mistaken in identifying Jesus as “God” (the Son) in the above verse, then presumably you also believe that the (non-Trinitarian) Jews were mistaken in their offense against Jesus, here:
John 10:33,39 AMP
The Jews replied [to Jesus], We are not going to stone You for a good act, but for blasphemy, because You, a mere Man, make Yourself [out to be] God.
…They sought again to arrest Him, but He escaped from their hands.