Where did you cut yourself? It all depends, if it was your wrist you might have cut a veins.
If not well then its not that serious.
But as for the bleed your blood is made up of: red blood cells, white blood cells and platelets.
The platelets gather around the wound and block it up do no more blood can escape. But they best thing to do is to get a damp cloth, a dry cloth, bandaid, some rubbing alchohol or peroxide.
What you do it press the damp cloth on it and while the cloth is soaking up all the blood the water will kinda clean it and the perssure will make the blood flow slow down. Then after about a minute take it off and get the alchohol or peroxide and pour it on the oppposite side of damp cloth you used then pres that side on the wound. I know it'll sting like heck but it has to clean it out.
Do that a few times until the burning stops, then take the dry cloth and and wrap it around the wound tightly but not too stop. Enough pressure to stopp the bleeding or at least slow it and after a while like the next day it should have been stopped bleeding and is healing. Keep it clean and once it stopped bleeding cover it with something to keep infections out and something to hide it from your parents if you're that worried about it.
I hope this helps. And please stop cutting yourself. I know how you feel but let time heal you.
Here is a link to help you out.