No, dizziness wouldn't be related to breast cancer. Could be caused by some medication .... I know you mention that you haven't started Chemo but I was thinking you might be on some other medication.
I have never heard or read of dizziness being a symptom of the cancer itself, but certainly being diagnosed and trying to understand all of the treatment options was enough to make any person dizzy. I believe dizziness is a symptom of stress. You'll want to report the symptom to your doctor, but be sure to give yourself some rest and relaxation time.