Can a 17 y/old without a child use the mirena (levonorgestrel)?

Gotta see GYN. Please visit your gynecologist. I assume you're sexually active, so birth control, as well as sexual health are necessary items to discuss with gyn. Your anatomy and physiology as well as menstrual history are important variables that only your gyn can guide you with.
Yes. For many years the common practice was to avoid IUD's until after a woman had children. More recent practice, has changed. Initial insertion is uncomfortable & the product pricey, but the passive nature of protection for years at a time make it a reasonable choice for many women. Only your personal doc can decide if it is right for you but it is not uncommon to use in teens now.