The first is correct, but awkward. For the second, you probably meant to write "I have been taken over by tiredness." This is also correct, but awkward. It is much more natural to use the word "overcome." "I am overcome by tiredness." And I think it is even more natural to use "fatigue" instead of "tiredness:" "I am overcome by fatigue."

Best to say: I'm tired. I'm absolutely shattered. Or, less frequently I was overcome with tiredness.

You can also say "I am exhausted".

If your goal is to sound natural, I would recommend: I'm really tired. I'm really worn out.