So I'm more than likely going to repeat what other people have said in this thread, but hopefully add some personal experience to the matter.
When I was younger, and I got bored at school, I'd occasionally mess around with school computers in a script kiddy way quite literally. It was simple, because our school IT staff were inept, doing such student stuff such as leaving default passwords for remote management software or having user accounts of the IT guys themselves passwords being suceptible to dictionary attacks, or other stupid things like not checking that the password in the configuration files for a Windows unattended install were encrypted, or that we couldn't directly access those files from none IT-staff AD accounts.
So needless to say, one boring day I made the mistake of using one of the network administrator accounts to make changes to the school. In a stupid sense I thought I was being helpful, recompiling adblock to be able to better distribute it on our network, ensuring WSUS was configured properly because a lot of the public facing servers were unpatched, trimming down on network overhead during logins and the like.
Well, for some stupid reason - I decided to be honest and tell them what I did (its important to know, I had a rather good relationship with the IT guys at this time, well - we'd talk about games and conventions and have a laugh when we met and such, but being mere acquaintances doesn't save your back when their jobs are on the line, nor their respect from the rest of the school).
And that's how I ended up almost facing charges under the UK computer misuse act at age 17/18, which is indictable and can carry a heafty prison sentence, so I almost ended up with a criminal record, prison time, and a fine, all over what I thought was basically me learning and being useful, but realistically is a massive deal to the school.
It wasn't the IT department who were the ones who'd kicked me out of school, they didn't want to. They were very annoyed with what I'd done, after all - I threatened their very livelyhood, they could go to prison themselves for negligence on data protection. But the headteacher had a reputation to upkeep, how bad would it have been if I ended up in the news and then the school is under investigations, heavily fined, the head is fired, etc.
At the end of the day, I got insanely lucky. Why? Because I grovelled, and pleaded, and begged to not be punished as badly as they legally could have done. And that's important, because even if you don't feel like you've done anything wrong, you are not in a position to say otherwise.
The fact you didn't sign the agreement policy doesn't make you immune from their actions, it makes EVERY time you've used the computers at school a crime, as you did not have permission to do so. if you mention this to them, and they decide to prosecute you legally, this will be brought up in court and you've commited a crime and they have proof of it straight up. It's not worth arguing on this point. They might not have ANY proof of what you have on the USB stick being either malicious or otherwise, but they WILL have proof you were using the computers illegally because you did not sign the policy which means that basically you've been using the computers entirely without permission.
Take it from me, be humble, and lie. You're two weeks away from your finals, don't ruin your chances over this. Say you didn't think what you were doing is bad, that you didn't cause any harm both intentionally and recklessly, but you understand how they're acting.
Accept the light punishment, and be banned from the computers indefinitely if thats what it takes. If you be cocky or aggressive about this, I'm unsure about US law specifically, but you risk actual prison time over something this stupid.
Sorry for the long read, but hopefully my perspective on this situation has helped you somewhat. I eventually got back into school with no access to the network at all forever, and that if I did try and gain access the school were very clear that criminal charges would be brought against me. And I coped fine, and in September I'm now going to university/college - that wouldn't have been possible if I'd have been aggressive on this issue, I'd have not even been typing this, I'd have been in prison. So be sure to be humble in the whole matter.