Why do English translations (NIV, etc) say "us" and "our" in Genesis 1:26 and Genesis 3:22 but the Hebrew doesn't say that when viewed with an Interlinear version?
The “of us” and “our” are present in the Hebrew. In Genesis 1:26 what is translated as “in our image” parses as follows:
בְּ – in (the same letter as the first letter of Genesis 1:1)
צַלְמֵ – image (shadow)
וּנ – our (of us) [you will also see these letters regarding the Hebrew of “our likeness”]
Literal rendering of Genesis 1:26 might be “In shadow ours”
In Genesis 3:22 you will see the words below:
כְּאַחַ֣ד – as one
מִמֶּ֔נּוּ – of us
Hoped this helped
The word "image" in Genesis 1:26 and 3:22 has appended to it (as is the norm when denoting the possessive in Hebrew) the letters נו (pronounced nu), making the word not simply "image" but "our image." You may recognize this ending from the famous Jewish 'creed' the Sh'ma: "Hear O Israel, the Lord is our God: the Lord is one." The word "God" here has likewise appended the letters נו (pronounced nu). That is, "eloheinu" ("our God").
This contextual usage of the word is not considered in some interlinears (and even when it is, it assumes knowledge of the Hebrew language sufficient to recognize how the translators treated the original Hebrew, which may on a literal level, mean something quite different: e.g. "nose" being translated "rage" or "anger").
To make it clearer what others are saying, here's an example from Blue Letter Bible.
Notice that the column heading says "Root Transliterated". I.e. it shows the root Hebrew word, not the word as it is actually used in the text.
The roots are listed as "צֶלֶם" and "דְּמוּת", while the original Hebrew verse at the top says "בְּצַלְמֵנוּ כִּדְמוּתֵנוּ".
If you look at only the words in the table, you'll see only the roots, and will miss the grammatical prefixes and suffixes (in this case meaning "in our" and "after our").