Getting on bc without parents knowing

I want to get on the pill without my parents knowing, (I'm 16 btw), but my main concern is insurance issues. I believe I'm on my dad's health insurance plan, and would like to know if planned Parenthood (or any clinic) would allow me to pay out of pocket. Because I really do not want my parents to find out, and I don't want to deal with insurance. And is there a way to still get the pill free without insurance? Sorry if I seem stupid, I'm just really paranoid about my parents knowing I'm on BC and I don't know exactly what to do. If it helps, I live in Texas.