24 yr old on conservative religious parents’ health insurance

Hi! Not sure if this is the right place to be posting this. I grew up in a highly conservative christian household; my parents are vehemently anti-sex, anti-choice, anti-alcohol, anti- “things of the world”, etc. I am a 24 yr old adult living at home post-grad until I have saved enough money to move back out. I am on my parent’s health insurance until 26. Dad is a doctor and mom is a nurse. I recently had my annual women’s exam at the OBGYN (I am not concerned about them knowing I had an annual exam). But I did test positive for chlamydia & BV and subsequent prescriptions were sent to my pharmacist by the OBGYN. At the pharmacy, I asked for them not to bill the medications to my insurance and I paid for them out of pocket instead. However, the pharmacist did let me know that she had to go in and “un-bill” the meds to insurance and instead give me the full bill. I am already a high anxiety person and having religious parents who do not support sex-positive education or reproduction freedom has been very hard for me. So my question is this:

Will STD test results show up on my EOB that is mailed to my house? (I have CBA Blue insurance, an affiliate of BCBS, and I do not trust my parents to NOT open my mail lol) Will it show up that I paid for medication out of pocket if it was at one point billed to the insurance initially?

Thank you so much for any and all advice.