Yes. Modern HIV tests are very accurate.
This accuracy has to be considered with the window period.
For example, 4th generation tests will pick up 95% of infections at 28 days after exposure.
A confirmatory test three months after the exposure is always recommended. This is because 5% of people take this long to show a positive result.
A positive test result is routinely confirmed using a different type of test called western blot. The western blot test looks for immune responses to specific HIV proteins.
When used as a confirmatory test, the western blot result is 100% accurate. (This assumes that there is not a lab error and that it is your sample that has been tested).