Spontaneous nose bleeding (epistaxis) is usually not a very serious condition and stops on its own. In rare occasions, nose bleeding can be very intense and a person might need intervention (tamponade) and assistance provided by an ENT-specialist.
Acute blood loss can’t be compensated with any kind of food. The body can compensate for such easy bleedings by itself. If the bleeding is heavy with great blood loss (more than 1 liter), which is not in your case, a person needs intra-venous infusions and blood transfusion immediately to prevent hemorrhagic shock, beside stopping the bleeding.
Chronic (repetitive) bleeding does not cause shock but causes iron-deficiency (sideropenic) anemia. Besides treating the bleeding, anemia is treated with iron supplements. Some foods that contain iron are recommended in those cases.