If you find yourself with a bleeding nose, do not pick your nose, it will only make the bleeding worse.

I have heard many recommendations, including the "roll a peice of tissue paper up and shove it up the nostril" method to the "blow the blood out through your nose until there is no more blood to blow" method. The tissue paper method will usually work, however, I do recommend placing a cool cloth on the back side of your neck. Place your index finger and your thumb on the middle of your nose and lightly pinch. Lay down on your back if you can.

As someone who has had at least several thousand blood noses in their life, I can offer a couple of tips from personal experience:

If the bleeding is relatively minor or slow, it is possible to keep it in check by lightly and consistently sniffing, not enough so as to draw blood into your sinuses, but just enough to stop it dripping. The airflow also speeds the clotting, and it involves no use of unsightly bloody tissues.

If you're anywhere near a sink it can also be beneficial to hold the bleeding nostril under cold running water. I've found this is best when the bleeding is out of control (as a result of excessive heat or high blood pressure, two things that invariably result in nasal haemmorhage for me).

For all levels in between, the tissue plug or fingers-as-pegs methods are both adequate. Where you hold your head is pretty much irrelevant, but I don't recommend a position in which the blood can flow into your sinuses, for this is very unpleasant. Don't hold your head back, and I personally wouldn't suggest lying down on your back either.

If you go to a hospital for a persistent nose bleed they will give you a small amount of cocaine to stop the bleeding.

I think this is because cocaine contricts blood vessels and prevents the flow of blood.

It is probably possible to use this method at home should you have a small amount of cocaine on hand, but be forewarned it may lead to a nose bleed addiction.
The following is an excerpt from The White House Cookbook published in 1887:

For Bleeding at the Nose

Roll up a piece of paper and press it under the lip. In obstinate cases, blow a little gum arabic up the nostril, through a quill, which will immediately stop the discharge; powdered alum, dissolved in water, is also good. Pressure by the finger over the small artery near the ala (wing) of the nose on the side where the blood is flowing, is said to arrest the hemorrhage immediately. Sometimes by wringing a cloth out of very hot water and laying it on the back of the neck, gives relief. Napkins wrung out of cold water must be laid across the forehead and nose, hands dipped in cold water, and bottle of hot water applied to the feet.

My doctor told me to do the following:
  • If you've had a bloody nose in the past day, and you've got another one, blow your nose first. It will get the old clots out and provide a fresh surface for the new clot to form
  • Pinch your nose -- not too hard, but enough to seal the nostril shut and give the blood time to coagulate.
  • Don't tilt your head back or lie down. It will cause the blood to get into your sinuses or into your stomach (blecch), which can make you sick.
  • Don't pick at it or it won't get better. (and it's rude, too.)

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