Actually, there is a verb "to be up to smth.." and it means "To be equal to, or prepared for" (from an online dictionary).
For example: he is up to the business, or the emergency.
or, there is another meaning "To be engaged in; to purpose, with the idea of doing ill or mischief"
For example: " I don't know what he's up to."
So, as you see both verbs have a similar meaning.
In your first sentence I would say: "I am really not up to it"
In the second sentence I would leave it as you wrote it.
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