NO you dont sound unhinged at all you sound like a worried mummy, that is all
It sounds very much like she might have an infection. Either a uti or some kind of thrush.
I used to suffer terribly as a child, and mum took me regularly to the Gp. I had horrible discharge once, with a uti. Blood in urine, and just a nasty puss also, from the urethra. Mum was never talked to about SS. I was on almost permanent anti-biotics. It was really miserable at that age.
I remember going to an out of hours GP once, when I was about 5 or 6 maybe? As I had a raging temperature, and unbearable pain with cystitis. She wanted to do a thorough examination, due to the reasons you suggest. I was SO upset, and felt so incredibly violated, as such a young age, I've never ever forgotten it. ( hence being able to recall the incident from so young)
Mum made a complaint to the Local H.A. She was informed at the time, that it was very unusual practice, to even consider such a thing, straight away. It should NOT be the first thing, thought of in such instances. especially as I had a long history of confirmed UTI's on my medical records. It should be a very very long way down the list of possibilities and when there are other things that would give the Dr those concerns.
I'm telling you about this, not to worry you more about it happening to your daughter, but to reassure you that it really is SO unlikely.
The biggest lesson to be learned young lady DO NOT RESEARCH HEALTH PROBLEMS ON THE WEB YOURSELF ok??
Do hope she is ok, poor little love, I really really do empathise.