Planned parenthood questions

Kali • 17 and ready to sleep 😴
Ok my period is late by 5 days and I have no symptoms . I'm tired of feeling stressed everytime I'm late and I want to look into birth control (besides condoms which is what I use)
Would planned parenthood show up on insurance ? I can not have my parents find out and I am under their insurance 
I really can't afford it how cheap can it get down to with insurance ?
Also how expensive are their pregnancy tests and what do they do or should I just go get one from Walgreens