I've had nose bleeds that lasted for more than an hour, I'm still alive! However, don't put your head back, the blood runs down your throat into your stomach, and for some reason I don't understand, that's not good for you. Bend over a bowl or sink, pinch the bridge of your nose a little out to each side and slightly into your eyebrows; this is an acupressure point and sometimes stops the flow immediately. One thing I used to do was put a proper size chunk of ice in the side that is bleeding and that slows down the flow. If you have bloody noses repeatedly, get the blood vessel cauterized. (Burned shut). It stings for a minute or two, but is really, really worth it to get rid of the nuisance bloody noses. I see no need to seek medical help unless it has been 2 or 3 hours. That's what the triage nurse told me. You're fine, don't let the reactions of others frighten you. I'm not a medically trained person, I speak from experience. Good luck.
Go to the emergency room. Have you kept your head tilted back and held a cold, wet wash cloth against your nose? If you don't keep your head back it may be hard to get the nosebleed to stop. If you've tried that and it hasn't worked, seek medical help immediately. 20 minutes is way too long to be bleeding like that.