thanks for being here and asking questions that help you come closer to the God of Israel. I'll happily help you with this one.
Generally, we base all our understanding of the Torah on the commentaries. Please see this answer as to why the commentaries are necessary, and where they come from.
There a couple of commentaries1 that reach your conclusion, but not by the way you arrive at it. They base it on the hebrew word היה, which is past tense, so they read it "behold Adam was like one of Us [and he is no longer]".
Generally though, the commentaries interpret the words to mean that Adam has indeed become like God, because he knows good and evil, which animals and other forms of life do not share. E.g. Rashi:
היה כאחד ממנו IS BECOME LIKE ONE OF US (or, like the Being who is
One, Unique amongst us) — Lo, he is unique among the terrestrial ones,
even as I am unique among the celestial ones. And in what does his
uniqueness consist? In knowing good and evil, which is not so in the
case of cattle and beasts (Genesis Rabbah 21:5).
The phrase כאחד ממנו doesn't translate the way you have proposed. It is literally translated as "like one from us", or in more technical logic: "He is similar to one from the category of those that we count ourselves among". This category is "those who know good and evil".
If you are quite technical with your understanding of the hebrew language and grammar, you might find this Ibn Ezra a good read into understanding how this pasuk is working, and it deals with all the words you question.
tl;dr: there is a tradition that this means we lost our status as being "similar to Him", but also a a tradition that we became more similar to Him. The way we resolve that is to realise that both are true. On the one hand, we developed the ability to internally appreciate good and evil, which is a status only shared with Hashem, but on the other hand, having that appreciation of evil in a physical body activates an urge to do evil, and cause him to chase the material rather than the spiritual aims set for Him when God made him in the Divine Image.
1 - e.g. Sforno, Rabbeinu Bachaye