Abnormal Menstruation Since Age 11...Unexplained. Any suggestions?

I began menstruation at age 11, and I have always been irregular. I began birth control at age 20, and went off and on the pill. I have heard that going off and on is very dangerous. But, when I am off the pill I NEVER see my periods even after the suggested wait time of about three months. I don't have abnormal bleeding or even period symptoms. It upsets me that every doctor I've been to refuses to give me an ultrasound so that I can rest my nerves. They just want to keep sticking me on the pill. That's like "a fake period/quick fix" and I want to have kids one day. Not pump my body with these hormones so much that it becomes dependent. The last time I saw my period it stayed for a week or longer and I was just getting off the pill and before that I saw it three months earlier and it was very painful and I had JUST went back on the pill. That's why I stopped.

Why does irregularity happen? Are there any alternatives besides the pill? I had my hormone levels checked for hyperthyroidism and they said they were fine. Thank you.