STD testing insurance questions

So I’m gonna start this off by saying I am 23 and I’m very well aware of what I should do however, I just want some advice. I’ve been with my boyfriend for 4 1/2 years. There’s never been a time that I’ve cheated. We have had Issues in the past with him and his loyalty. I’ve only ever known of anything that’s been verbal between him and another person. lately, I’ve had some weird cycles with light blood and brown discharge too. I kind of want to get tested for any STDs. This might be normal but idk. I’m wanting to know if y’all know if on insurance it tells you what test were done in the claims. I only ask because I’m still on my parents insurance and I really don’t wanna freak them out right now. I can go get testing and pay cash for it. I would just like to not spend any money if at all possible. Any guidance or recommendations greatly appreciated.