I believe you're talking about the IUD, the most common one called the "Mirena" IUD. IUDs are not typically recommended to women who are childless. It's harder to insert into a woman who hasn't given birth. You can certainly ask about and I encourage you to try, I had a Mirena and I really liked the freedom I felt with it (not having to remember things, change things, repeatedly buy contraception, etc), but just don't be surprised if they're unwilling at your age.
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Holly.
Mama to Hunter Kai