HIV testing. Yes. Of course it is. That is as long as you have allowed enough time to past for your body to produce antibodies against the HIV if you are infected. If you are not infected then if you only test with the HIV antibody test, you must wait six months after exposure for it to be fully reliable and accurate if you test negative. The situation in reality is that no one need wait that long .
Accuracy of ELISA. The elisa test is 99+% accurate (sensitive and specific) in individuals who have had the infection long enough for the assay to pick it up. For the 3rd generation tests used today, it can reliably detect individuals infected w/hiv at approximately 15 days. The 4th generation wh/tests for HIV antigen and antibody may show results even sooner. Always have testing done at a reliable certified lab.