Don’t believe everything you read, even on StackOverflow. Computer timing functions are “precise” to microseconds, as far as that goes. The limiting factor on “accuracy” is really more about your coding and when you call that function with respect to the event you want to time.
Firstly, you need to be careful to distinguish between precision and accuracy: they are not synonyms.
Secondly, we can’t give you any guidance at all without knowing the details of your code.
It is true to say that PsychoPy has micro- (rather than milli-) second timing abilities. It is also true to say that you can write code in PsychoPy that will yield grossly inaccurate and imprecise timing.
Lastly, I’m not sure how many people here know much about OpenSesame. The PsychoPy advice we give here may or may not be useful to you in that environment.
So come back to us with more details and we’ll see what we can do.