If it's only been 2-3 weeks since your last period, then probably not. If it's been 2-3 weeks since conception, then it could be accurate, but again it's still really early, so it's better to wait. The best time to test is if your period is at least a week late (or more), or if you are really concerned, have a doctor do a blood test.
A home pregnancy test will show positive if you are 2 to 3 weeks pregnant. The pregnancy test should not be done until the last day of your period. This is because pregnancy can take place some few days after conception.