My 8-year-old niece recently had a cut on her finger from a broken glass that wasn't deep at all but wouldn't stop bleeding for almost half an hour. I put pressure on it, but every time I took the pressure off it would bleed again. She's healthy and hasn't ever had any bleeding problems before. I would have felt silly coming to the emergency room for a cut that wasn't much deeper than a paper-cut. It eventually stopped and she healed normally. What could I have done differently at the time?
The first step for most minor bleeding is to put significant pressure directly on the site of the injury. For a cut, this is directly on the wound.
For a nosebleed, this would mean pinching together the nostrils (not pressing on the bony part of the nose higher up, which is useless). This direct pressure technique usually works great, even for fairly big bleeds.
Most people know how to apply pressure but don't know any other tricks. Here's a good one: use gravity to help stop bleeding. Raise the injury as far above the level of the heart as possible. Elevation reduces blood pressure and blood flow, letting the clot survive long enough to plug the cut capillaries.
The wrong thing to do (and I see it all the time) is for a patient to keep their injured arm in their lap or their cut leg down low on the floor and wonder why the oozing won't stop. The force of gravity combines with the patient's own blood pressure to break the fragile clot or will not allow a clot to form in the first place.
Apply pressure and get those wounds elevated above heart level if you want them to stop bleeding more quickly.
Now, there are also considerations such as whether there was an embedded piece of glass still in the wound (we often X-ray these if the wound is deep); whether she has a clotting disorder (very uncommon); and is she up to date on her tetanus (hopefully). Only you and your doctor can sort these questions out.
And finally, if direct pressure and elevation aren't working (or if you're on aspirin or have a dirty wound) see your GP or go to the ED, that's what we're there for.