I did about the same thing sharpening a 9" chefs knife for my mom. Finishing touches, holding the stone in my free hand and took the top of the last knuckle off of my middle finger. Grabbed some paper towels and tried to hide it from her but that didn't work out, and she got all upset when she found out your run of the mill 1/2" wide bandage wasn't going to do the trick.
The cut was so clean, it just wouldn't stop bleeding. I guess the body doesn't register enough trauma and doesn't shut stuff down when you get cut on something that sharp.
The only way to calm my mom down was to agree to go to the emergency room, and of course I wasn't allowed to drive (in fairness I probably would have hit the gas station for some super glue and then grabbed a burger so I didn't get back home too soon) and my uncle got drug into the mix

I soaked through 2 handfuls of gauze in the waiting room, before they finally took me back.
The nurse unwrapped it and threw the bandages away. Then proclaimed that I was definitely missing a peice. I had stuck the peice back on before I wrapped it up, and told her so, and before I could protest she proceeded to dig it out of the trash can and stick it to her clipboard like a hunk of chewing gum

I was ready to leave at that point, because I would sooner cut the rest of my finger off then let them get that hunk of skin near it again.....but luckily the doctor showed up and said to throw it out again.
Long story short they dumped iodine on it to stop the bleeding and put a splint on my finger I was supposed to wear for 2 weeks or something. That lasted about a day and a half and then I was back to a couple band aids, supplemented with electrical tape when I was in the shop.
I guess the point I'm getting at is that iodine will stop the bleeding (I think its because the initial shock also temporarily stops your heart......).