I had something similar happen to me in the final week of teaching art class before summer vacation.
There was this trolley I used to lug supplies between classrooms which I had decided to clean. Halfway through scrubbing one of its shelves I brushed past one of the metal bars that had previously been welded. Unbeknownst to me the weld had ruptured leaving me with a deep cut when I went past it.
So now there was blood gushing out of that finger onto the trolley and the floor.
This was past school hours and I was one of the last people around. No one nearby to get the first aid kit for me. The stupid thing was, normally I have one in my classroom, but it has to be kept under lock and key because it's a special needs school. And wouldn't you know it one of my colleagues had forgotten to return that key.
Now I had to dash through the hallway to administration where I knew they had a first aid kit.
Once I got there though, I couldn't find the damn thing.
Long story short; eventually I found it hiding in some closet, but by that time I had bled over several doors, the hallway and the entire administration office, even leaving bloodstains on some important looking paperwork there.
The finger didn't need stitching as it wasn't even that bad of a cut, but for some reason it just bled like nobody's business.
Worst part was cleaning it all up. I never did get the stains out of that paperwork.