Looking at Old Testament poetry. It doesn’t use rhyme and meter but uses other poetic devices. There are three main types of ancient Hebrew poetry. These are discussed below –

Synonymous Poetry – two lines that say nearly the same thing but want to stress what is being said. For example this is common in the Psalms as in

Psalm 19:1
The heavens declare the glory of God;
the skies proclaim the work of his hands.

Antithetical poetry is the opposite – it uses successive lines to say two different things, each relative to the same theme. You’ll not only find this in Psalms, but all over the Book of Proverbs, such as –

Proverbs 17:22 –
A cheerful heart is good like medicine
But a crushed spirit dries up the bones.

Synthetic Poetry uses successive lines to build to a point, systematically showing or convincing the reader. Here is an example from Psalm 139 verses 1-6 …

O Lord, you have searched me and know me!
You know when I sit down and when I rise up;
    you discern my thoughts from afar.
You search out my path and my lying down
    and are acquainted with all my ways.
Even before a word is on my tongue,
    behold, O Lord, you know it altogether.
You hem me in, behind and before,
    and lay your hand upon me.
Such knowledge is too wonderful for me;
    it is high; I cannot attain it.

You can use these techniques in your own personal poetry creation. And of course you can include rhyme and meter too.

Reference – more details can be found on this site … https://mysonginthenight.com/songwriting/how-to-write-a-personal-psalm/