Unless OP's parents are medical billing coders, they won't be able to decipher those details.
There is NO billing code different for what happens in the doctor's office. It's simply how long you're there.
And the lab work is going to be acronym soup, none of which will contain the letters "STD", "STI" or "HIV".
An EOB (Explanation of Benefits) may mention prescription drugs, but what are the odds your parents know what
If they did include such things, they are violating HIPAA, because USPS is not considered a secure channel for transmitting confidential patient care information.
Get over your fear and see a doctor, because that window of opportunity has almost closed. The free clinics are probably not going to work (has everyone forgotten it's the holiday season and everything is running reduced hours?!), so you're going to have to suck it up.
You'll likely be given a rapid test and will likely be discouraged from seeking PEP.