You have an interesting story here.
I've never read a fic in which Minerva is paired with Tom before (There may be others but I haven't read them.) The idea has lots of possibilities. I like that she's Quidditch Captain, I like that she notes his lack of excitement when sorted.
I think you did a good job of capturing Tom Riddle. While he's piercingly cold in canon, I can see him having, in his youth, used his and other people's bodies for pleasure, and in a rough, self-serving way.
I am not sure I can see him admitting to murder, and I am fairly certain he'd have killed anyone who knew, but Minerva does make a good point when she says he would know if she told.
I find Minerva less convincing. Iit's not her wild sexuality - I can see that.. It's this - Minerva McGonagall is a woman who seeths with righteousness in the face of evil, and I cannot imagine her keeping the secret of Tom having killed those Muggles.
I can imagine that she told someone, at least - Albus Dumbledore, perhaps, if she felt the Ministry wouldn't do anything - or I can see her becoming, over the years, twisted inside from not having told, but I cannot see her just keeping it quiet. To do so would be against everything I know about her..
It's a good story. If the woman was Minerva's friend, or her sister, or some other person we know less about, I could see it. I just can't see it with Minerva herself.
Oh, in the first paragraph - her body being full of wind... could be taken as a flatulance reference which is not what you are going for. Same sentence, Air might work better. You're going to lengths to describe her elation, so you probably don't want to distract your reader from that.
Overall the story has many good points. I'm just not personally convinced about Minerva keeping her mouth shut.
That was a little shocking. I guess I never thought Minerva would be involved in something like this. She seems to always have been the older, sensible person. Fascinating story.