Cervical cancer does not run in families. So even if every woman in your family had cervical cancer, it would not raise your risk of getting it. Cervical cancer is from the hpv virus.
You are seeing a doctor, that is excellent! Abnormal cells on your cervix .A.R.E .N.O.T cancer. They can progress to cancer (doctors estimate this process takes a very, very long time. Like years and years) if left untreated. You are being treated.
What does your doctor recommend at this point? Another leep or a watch and wait approach?
Good luck!