I had nosebleeds as a child and ended up in the ER also.
The reason the nose bleeds is because the surface cappillaries in the nasal passages are broken. The reason for the breakage is usually caused by dried nasal mucousa that crack and therefore bleed. The top offenders for causing nasal drying are many but the top offenders are allergies, medications, and environmental. Most people that have allergies take some kind of antihistamine that helps to stop allergy symptoms like runny noses and itchy eyes. But if your nose isn't running, the medicine doesn't stop working. So, if you are normal today, the medication will still dry you out. If you have a runny nose that is ok, but if not it can really dry you out more than necessary. Second, medications. More medications besides antihistamines (like benadryl, zyrtec, claritin) can dry out mucous membranes of the nose and throat, like robitussin in liquid or tablet form. Ones that usually help "dry" up a cough. Well they are drying out other things also, like your nasal passages. Then there is the atomsphere. If you live in an extrememly dry climate, little outside moisture, run the A/C alot, or are a mouth breather...all these environmental things can dry out the nasal passages and mouth/throat.
Now, I am going to tell you what we do at my house for me and my kiddos. I am also a nurse and can tell you these things work. But only do what you feel is safe for you to or what you are comfortable with.
The first things we do is pinch the nose at the bridge between the eyes to help staunch the flow of blood. I recommend leaning the head forward, becuase you will be tempted to swallow any blood draining down the back of the throat. Swallowing to much blood will make you nauseated. You definately don't want a kid to be throwing up and bleeding!! Then we apply ice. We try hard not to blow, pick or dislodge the clot that is forming. Then when the clot is formed and the flow has stopped, I try to get the offending child into a warm bath with steam or near the cool mist vaporizer to get some moisture up into the nose. We will also use a q-tip to apply a small amount of vaseline in the nasal passags just within the nostrils, this is to help keep them moist. DO NOT STICK THE VASELINE Q-TIP UP THE NOSE!!!! We also use Ocean nasal spray to moisturize, or any generic normal saline nasal moisturizer. We also increase oral liquids. Continue with our antihistamines.
If the bleeding doesn't stop I would recommend a Neo-synephrin nasal spray. The neo spray constricts the capillaries in the nasal passages, thereby stopping the bleeding. It is what we used in the ER. It is over-the-counter in spray and drops. I think we even saturated packing for severe cases. We like the spray. I would suggest that you don't use packing at home, that is for a doctor to do. You can gently insert the tip of a small tampon just inside the nose if you are worried you are bleeding to much and need to go to the ER. Again, not shoved high into the sinuses, just in the tip to catch the flow.
If your daughter gets them alot, I would invest in a bottle of neo-synephrine. If you really feel that she has severe allergies, I personally have found great relief from rhinocort nasal spray. It is a prescription that is a very low-dose steroid sprayed directly on the nasal passages. It helps keep those little capillaries and nasal passages from getting so inflamed and irritable. It also helps with the nasal drip by local medication, and not such drying things as antihistamines, that are systemic. I have found that I have less nose bleeds, less runny nose and less sinusitis and sinus infections on this spray. My primary doctor said it is such a small dose it is safe to use for long periods of time. It is also not really enough to be absorbed systemically. I have severe chronic allergies and was originally prescribed the spray by my ENT/allergist. And have had great success. I know my 13 year old has had a precription for severe seasonal sinusitis, but not a long standing prescription, so I am unsure of the length of use in children. But do know it works for us.
If you find that she continues to have severe or frequent nose bleeds after the neo-synephrine, I would advise you to see her doctor to have her evaluated for allergies, adenoid problems. I would think that you would need more severe ones to have anything cauterized, but you would probably already be at the ER should that happen. I would also advise you to keep a journal of the bleeds and steps to stop them for the doctor to evaluate them if you are very concerned. That way you will have the information handy when you visit. He can then evaluate what is not working and go from there, perhaps a referral to a pedi ENT.
I think the main thing would be prevention at this point. And neo-synephrine to help stop them once they have started.
Good luck, You might also invest in some oxy clean to get the stains out. LOL.