Thanks for your post. I can understand why you would like to know why you are only getting 2-3 periods a year.
Do you feel any irregular pain or heavy bleeding during the times you get your period? Many times irregular periods are common in teens but tend to regulate slowly over time. Sometimes they remain irregular but this doesn't necessarily mean there is something wrong with you. However, I would continue to press for answers because in the two instances that I've known women with irregular periods, they have both been cyst-related, this shouldn't scare you but asking for a pelvic ultrasound doesn't sound unreasonable to me.
Good Luck, I hope you get some answers soon. Remember that if any particular doctor seems dismissive to your concerns you are always entitled to change to a different doctor.