The difference between "I'm sick and tired of..." and "I'm getting sick and tired of..." lies in the level of frustration and the timing.
"I'm sick and tired of..."
This phrase suggests you've already reached the point of frustration and are expressing that you are fed up with something. It implies that the situation has been bothering you for a while and you're done with it.
Example: "I'm sick and tired of cleaning up after you!"
(You’ve been annoyed for some time and can’t tolerate it anymore.)
"I'm getting sick and tired of..."
This version suggests you are approaching the point of frustration but aren’t quite there yet. It implies that the situation is becoming annoying, and if it continues, you will soon reach the point of being completely fed up.
Example: "I'm getting sick and tired of your excuses."
(You’re warning that you’re almost at the point of losing patience, but not fully there yet.)
In short, "I'm sick and tired" expresses that you're already fed up, while "I'm getting sick and tired" suggests you're on your way to becoming fed up.