The phrase "I'm tired" is a perfectly fine and commonly used expression in written English.
It can be used whenever someone is expressing that they are feeling fatigued or have a lack of energy. For example: "I've been working all day and I'm tired, so I think I'm going to take a nap."
Dictionary
i'm tired
phrase
Indicates that the speaker is in need of rest or sleep.
Exact(37)
"I'm tired, I'm tired," Bryant told him.
I'm tired of this.
I'm tired of it.
But I'm tired.
And I'm tired now.
"I say: 'I'm tired.
Similar(23)
I was tired.
I was tired mentally.
Always, I was tired.
But I was tired.
I am tired.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com