The Pill

okay, so I'm 16, turning 17 in a month, and I have a lot of irregular periods (usually ranging from one to two weeks late). it's always bothered me because I never know when to prepare and such. and now that I started having sex, it gets really scary when my period is late, even though we use a condom every time. I have tried to convince my parents to let me start the pill (they don't know about my sex life) but they always tell me that I will regret it because it will make my body go through undesirable "changes". what can I tell them to actually get them to consider the idea?