YES you can have an IUD.
I do not have kids, and I have never given birth.
MANY regular doctors will not do IUD'S... BUT Planned parenthood and other 'open minded' gynecologists will.
In europe, girls as young as 14 get IUD's because they are so safe and effective.
Can you buy alesse at a pharmacy? They do have a generic version. You may tolerate that hormone dosage the best.