Your language is Python, apparently. ( Please mention this. )

Yes, you need better time complexity than O(m). This is not hard - you don't need to test every single number up to m for being a Fibonacci number, do you?

If your code time out, you must find a more efficient method. I don't know how you calculate your complexity, but, seeing the submitted solutions, I have good reason to think your reasoning is inaccurate.

You can read the user-submitted solution from a file: https://github.com/Codewars/codewars.com/blob/master/docs/_recipes/testing/restricting-solution.md

Not sure if possible, but you could perhaps #define while cheat_detection(); while
It doesn't matter that that turns it into two statements, just as long as the cheat_detection() is called you will (silently) fail the test. Be sure to VERY CLEARLY state that 'while' is not allowed to be used ;).

If people know you do this they can work around it, of course.