The blood in dreams usually indicates the force of the life and energy that one is bringing while living the life. If you dream that you are injured at some part of your body, you should reconsider your health. The blood could also indicate that you are feeling tired. Perhaps youre working too much or have too many things to do at once. The blood that is coming from the other person could denote to the pain or problems that certain person is feeling and you know it. The subconscious mind is sending the message to give the help for this person. If you are bleeding because of someones fault, you will have disagreements with this person.
Read more about dreaming of Blood in other dream meanings interpretations.