Is it who we are or what we do that defines us?

Mum, wife, lawyer, Dr; these are all labels we place on people.  But what is it that defines us?  Bruce Wayne says "it's not who we are underneath but what we do that defines us" (I know it's from Batman Begins which isn't a literay great but it gets you thinking).  I am unmarried and have no children so immediately the first two arent even on the table; but should I define who I am by what I do??  In true Carrie style...
What is it that defines us as people?
For those wondering about the latter part of my blog title, has she recently got out of a nasty relationship, no...the Big C has been cancer, is cancer and is the latest thing which seems to be the label I cant shift from myself.  In July I was diagnosed with bowel cancer, I was 30 at the time with no family history so the odds were pretty slim.  Yes I would rather have won the lottery, but that was the card I was dealt.  I have never really thought of myself as having a label; the only thing I have ever labelled myself with is my job title and that wasnt really a conscious thought.  But now I just see a cancer patient.  At work, at home, watching the tv it just seems to be in my head.  Why do we feel the need to define ourselves, why the labels.  Is it true that what we do carries more weight?  I work hard, I care about my friends and family, I try to be a good friend, godmother, daughter and girlfriend aren't these things more important that a career choice or the fact we are married or not?  It surely should be more important that my special gift is growing tumours!
I am sure that with time I will see myself as I used to.  I will be the person I was, and hopefully be a better version with more insight.  The scars on my body are a constant reminder of the cancer but that is something I have, or had, and not what I am.