Are you sure they said a pap smear? Are you sexually active? If you are virgin, you don't need one and you are really young to have one anyway. They probably want an ultrasound instead. Or perhaps an internal exam. (which is similar to a pap smear). I would ask your doctor why he is recommending it. Also, don't listen to your mom, it's really your decision, unless there's a life threatening emergency going on.
Also, woman can get ovarian cysts at any age and they are really common.