Sad thing is, you probably would have been fine if you hadn't said anything. They can't afford to care about the how context of the situation.

My how things have changed. I made a working cross-bow in school. Got an A on it. Everyone carried a pocket knife.

should have just left it in toot pocket and forgotten about it

Just tuck it into the bottom of your backpack or hide it in a pocket where it won't fall out.

I was in a similar predicament, out adventuring with some mates but I forgot to take the knife/lighter out of my school bag. It fell out when we were just outside school in the smoking area and one of the other students cruelly told the teachers not only that I had one and apparently I had threatened him with it. I got in a bit of trouble for it and after it came to light that they were lying I was allowed back into the school to carry on with my studies.

Yo america stop freaking out about shit like this, and start freaking out about real shit

I'd like to think the police had the common sense to realise after you explained the situation to them that you were genuine and had no interest in bringing a weapon to the school premises! Hence why you offered it up to the school to protect yourself from any false accusations if it was to be seen by anyone! If you were looking to use it for defense or criminal purposes that's the last thing you would do!