Discharge from anus, should I be worried if family history of cancer?

Maybe. Go see your doctor and have yourself examined. It could be infectious and not cancer. Some viruses, such as hpv and HIV can lead to cancer.
Better to be safe. Any abnormal discharge from the anus should be a red flag. Although the discharge can come from something benign you don't want to miss something malignant. See your doctor for evaluation and possible referral to a GI specialist.