A lot of girls I have met who are also anorexic have cut in the past or still do so this info goes to you.
Before anything else, stop the bleeding. Put pressure on it with gauze, not a tissue because when the wound is clotting to stop the bleeding it takes in the tissue. Gauze is too thick. Don't bother checking constantly to see if the bleeding has stopped it will don't worry.
After the bleeding has stopped, clean up the wound a bit with just water.
Applying an antibiotic is alright but don't put too much.
Cover the wound and change the bandage daily.
NOTE- If the wound is deep and won't stop bleeding Please get medical help. Even if they put you on a suicide watch, it will only be for the fact you cut NOT the fact that you aren't eating. So make them think you just aren't hungry during the watch but still eat a bit to keep them away from the subject. You will get the help you need and no one will bother with your eating habits as long as you know what to say.