I agree, take the test and see where to go from there.
3 weeks late could be for a whole host of reasons;
Stress, illness, getting over Christmas or family crisis. All those things can delay ovulation massively and consequently a period.
Our bodies are strange things at times. Hopefully you'll get the answer you want. Will check back in later for your result.
If you are pg and 3 weeks late, then I doubt very much you'll need a sensitive test or FMU for that matter. It'll probably go +ve before it hits the control window