Honestly most dr's recommend an exam after the age of 18 or when someone become sexually active. This is because an exam is the ONLY way to detect cervical cancer. Also because your period is irregular it's possible they will want to do some sort of examination to make sure that everything is where it should be.
Sometimes though you can opt out of this, but I suggest against it. My grandmother opted out of a colonoscopy at 50 because she was raped from the age of 6-17 and didn't feel comfortable with it. She died of colon cancer in January. She knew she had symptoms, she ignored them, she avoided the suggested medical procedures and it grew to a point where she couldn't be saved. No matter the reason behind why this makes you uncomfortable your dr needs to be different. This isn't sexual contact, honestly I don't let my husbands hands wander anywhere near what my dr does. Because she's different the environment's different -so it's ok. Unpleasant, but ok.
At the very least I suggest being open with your dr- tell him/her that you're very uncomfortable with the idea of a pelvic examination. This might make them avoid it if it's just a precaution or help you through it if they feel it's something necessary.
Do you have a primary care physician? If so let him or her know about your periods he/she will most likely recommend it for you without doing a full exam. (That or send ya to a OBGYN.) That's how I got on my birth control I wasn't active at the time either. Also I am on the Nuvaring & LOVE IT! It may not be for everyone but I am so glad I don't have to remember a pill everyday b.c the fear of forgetting that & ruining your whole cycle is just as bad as not being on it at all except you flushed you money down the drain.
Hope this helps (: