While garlic does show a wide range of medicinal properties including potent antibacterial effects, it should not be used as an at-home cure or remedy to treat actual STDs. As Healthline points out, sexually transmitted diseases can cause long-term damage to your body if not treated right away and properly. Even though garlic has shown activity against some bacteria, it has not been proven to completely rid your body of the bacteria involved in STDs, meaning you could still be harboring the disease and risking damage to your organs and health if you rely on garlic alone.
According to the Centers for Disease Control and Prevention guidelines for treating STDs, each sexually transmitted disease has its own specific treatment that should be used, many of these only available by prescription. Left untreated, or not treated properly because of reliance on a home remedy, gonorrhea and chlamydia can cause infertility, and syphilis can be fatal (via Planned Parenthood). Those are not risks you want to take.