Cutting is NOT normal or healthy, nor are the fantasies you describe. Stop taking the untrained and ignorant advice of your boyfriend or parent, and go straight to a doctor. Do not pass go, do not collect $200. These are symptoms of SERIOUS mental disturbance.
I used to have a girlfriend who cut herself, probably exactly like you do. According to her, the cutting was to inflict a superficial injury, so that it could be "cared for". It wasn't about the cutting, it was about the feeling of being cared for. The cutting was simply a means to an end. This same woman had some serious emotional issues, initially diagnosed as "borderline personality disorder" and then rediagnosed to "intense, acute depressive episodes". Both diagnosis seemed accurate, from where I stood. The important thing is that these problems she had made it impossible for the two of us to have a healthy relationship.
As for the impulsivity, this is something I myself suffer from. For me, it is a part of ADHD. It may be for you also, it may not.
Check out this link: http://kidshealth.org/teen/your_mind/mental_health/cutting.html
this one paragraph stood out for me:
People who cut or self-injure sometimes have other mental health problems that contribute to their emotional tension. Cutting is sometimes (but not always) associated with depression, bipolar disorder, eating disorders, obsessive thinking, or compulsive behaviors. It can also be a sign of mental health problems that cause people to have trouble controlling their impulses or to take unnecessary risks. Some people who cut themselves have problems with drug or alcohol abuse.