An Intelligent student on the verge of expulsion uses embarrassing secrets he uncovered to prove his innocence when he is blamed for a missing classmate.    

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I don’t understand how using embarrassing secrets proves his innocence… ? To me, they’re not related in any way. ?The only way to prove his innocence is to prove he wasn’t involved – that involves his own secrets perhaps, but not necessarily any others (unless his own secrets involve others I guess).

Why is he on the verge of explosion? You’ve told us he’s intelligent not a trouble maker.

If the classmate has disappeared are the police involved? How is this student missing? Dead? Ran away?

I think writing something under 15mins is totally doable but the issue here is that the different components have no relationship to each other (yet). His goal is to prove his innocence – we need to know how he’s going to do that. If this is a serious crime, revealing secrets is simply diversionary and would suggest he’s actually guilty. His characteristic “intelligent” would be helpful if his goal was to solve the case but it actually doesn’t really tell us anything useful. If he’s intelligent then surely, to avoid expulsion, he just needs to do his work and get good grades…? Also, using secrets to manipulate other people isn’t a nice quality – he sounds like a bit of a dick to be honest. Why are the audience going to be on his side?

I think something like this would be better:

When he’s accused of being involved in the disappearance of a classmate, a popular teenager must uncover the truth to prove his innocence.?

There’s still issues with this such as why wouldn’t you just leave the police to do their jobs but I’m glossing over that for now. If he’s being framed, for example, it can neatly fill that in.

Personally, I think the whole embarrassing secrets thing doesn’t work as it has no relevance to the rest of the plot (as I currently understand it from this logline).

Hope this helps.