Body dysmorphic disorder is actually not really an eating disorder in the diagnostic manual widely used within psychiatry, the DSM-IV. Body dysmorphic disorder is considered what's called a somatoform disorder, or disorders that sort of involve preoccupations with health.
So, body dysmorphic disorder is where there's sort of an unusual fixation, a recurrent fixation, on a particular body part. As distinct from eating disorders, this doesn't necessarily refer to a concern about shape or weight. This might be like, I don't like my nose, my nose looks awful. Not only is there a recurrent fixation on something like the nose, but that tends to feed very dramatically and strongly into an undervaluation of self esteem so that a person starts to feel very poorly about themselves because their preoccupation with this body part is so intense. Body dysmorphic disorder, not surprisingly, as a result can be associated with other types of psychological syndromes like depressive illness, and the two things can obviously be related.
There are treatments available for body dysmorphic disorder. Like for many of the other syndromes in psychiatry, treatments can involve both psychotherapy as well as medications. Certainly, part of what shouldn't happen, or what you want to avoid if you suspect that you might have body dysmorphia or be overly preoccupied with a body part, is to avoid the urge to run to the cosmetic surgeon or have a quick fix for that body part.
What's known about body dysmorphia is that actually those types of procedures don't necessarily tend to remedy the body dysmorphia. People with body dysmorphia that are accessing cosmetic surgeons can actually be pulled into a cycle of repeated procedures because of such chronic dissatisfaction, and it's not something that a surgeon can fix or a cosmetician can fix. It's something deeper, more emotional, more about the psychology, and should be addressed by a mental health professional using either psychotherapy or medications, or some combination of both.