Black band-aids are the best! They stop the bleeding and the pain in seconds. Full of minerals and the power to shrink wrap bacteria out, they are perfect to keep in any kitchen or first aid kit. No need for adhesive. Read below...
Disclaimer: Do I really need one, folks? Go to the hospital if you are really cut. This is for a minor issue. Even though I've really cut deep, through my nail and this worked like a charm, please use your discretion to decide when a cut needs medical attention.
Nori sheet, cut into strips
Take effected finger and wrap all around with a strip of the nori. Then place in your mouth to moisten or gently rub some water on it to start the shrinking process.
Have you ever noticed how tight sushi is wrapped? When nori paper gets wet it contracts slightly making the sheet more durable and strong. Perfect to shrink wrap your finger to stop bleeding or just to hold the skin together so it can heal.
Watch the shrinking happen before your eyes. The pain should subside and even completely go a way quickly. The minerals in the nori help with that.
Now, don't get it wet. It will fall apart and you'll have to re-apply. I know nori is irresistible, but don't eat it either. It should hold up for a few hours to calm the situation down.