Child - could represent your inner self, or the child within. Alternately, it could suggest that you, or someone else in your life, is acting in a childlike manner (IE:: fits of temper like a child, being dependent on others for your own wellbeing...etc.). 

Nipples - relate to infantile needs and a regression into dependency. That they are your own, and being torn off, suggests a sacrifice you feel you are making for another....or you feel the need to remove yourself from a situation that is causing a dependency upon you.

Blood - Life's energy source. Love, passion, anger, and life itself...a vital part of our physiology and it may symbolize our strengths and weaknesses and our physical, emotional, and/or spiritual energy health.
If you are currently experiencing a very difficult time in your life, you may have dreams with bloody and frightening images. Don't worry, you may just be venting your fears.

Bleeding - suggests you are losing energy because of inner conflicts or waking conflicts. Feelings of being emotionally drained. It may also represent guilt. Dreaming about bleeding usually always points to the emotional wounds that you don't acknowledge.
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Do you feel that you are expending too much energy on someone, or something?
Is there someone in your waking life, that you feel is totally dependent on you, and you'd like to 'wean' them or separate from them completely?
Could there be someone in your life that is 'acting like a child', or have you been accused of acting like one?

Alternately...If you are a new mother, and you are breast feeding, this could simply be a dream caused by sore nipples. A condition that is frequent with new mothers, and

the fact that the baby is not latching on properly.

Hope this helps, best of luck!