Iphone 5s stuck on recovery mode?

I plugged my phone into my laptop and opened itunes and it said iphone in recovery mode and needs to be restored and updated. I clicked restore and update iphone and it took abou 2 minutes to extract files from the software. When it was done with tht, it said waiting on iphone and the apple logo appeared on the phone with the line underneath it. The problem is tht the line hasn't even started to fill up and its been at the same place for hours now… So what do i do? I've heard of tiny umbrella and fonepaw but i'm on my school's laptop and it won't let me download it unless i have the username and password for the admin, which i don't and i don't wanna do anything risky like going around the admin.

Qweqweqw

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