Back when I had braces myself, I faced the same problem. My orthodontist recommended Oral-B Super-Floss (don't want to advertise, but I just don't know a comparable dental floss). This indeed is perfect for use with braces, but normal dental floss works as well.
As mentioned by Trish Ling you can use brushpicks as well.
These are handy and easy to carry, so perfect for your scenario at school.
At home I had some kind of "brush stick". They look like this and probably are also available in the dental section of your local store, just as brushpicks are:
There may be no new insights here, but I just wanted to share my experience and save you from searching for images.
Keep in mind: All above methods best work in front of a mirror. So if you have to go to the bathroom anyway, brushing your teeth may still be the best solution.