Is it true that you only have two choices: to control your thinking or to be controlled by your thinking?

That is incorrect.
Why?
Only when there is an inner split (the observer and the observed) is there a desire to control your thinking.
The observer is equal to your thinking and when you see that directly, the inner conflict disappears. There is nothing left to control and no one can be dominated.
You are the world that you observe. In that lies inner peace.
There is no ‘you(r)’.