Hello,
Welcome to the ehealthforum and I am really glad to help you out.
Having such kind of itchy, bruise like rash is not a symptom of breast cancer. It can be due to an illfitting bra, an allergic reaction or skin conditions like hives, pityriasis rosea or dermatitis skin.
You should get this rash examined from a dermatologist. Since your mother had a history of breast cancer, it is better to get a mammography done to rule out any breast cancer.
It is very difficult to precisely confirm a diagnosis without examination and investigations and the answer is based on the medical information provided. For exact diagnosis, you are requested to consult your doctor. I sincerely hope that helps. Take care.