Yes, it is possible to have an STD when you haven't been with anyone. They're called STD's because they can and most often are transmitted sexually. Check out the Infection Section for more information.
Generally speaking, it's a good idea to start seeing a gynocologist annually once you start menstrating. This allows them to check your progress and have a good base line for later on. And, if you're sexually active, you definately should be seeing a gyn anually and getting tested for STDs on a regular basis.
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