Catherine, do you have a specific diagnosis of what type of liver disease you have? There are many different liver diseases. Your father's alcoholism would not contribute to your liver disease. There is a type of hepatitis that is caused by prescription medication. There is also an immune system disorder that causes liver disease. You need to find out specifically what your diagnosis is, in order to know the best way to treat it. Without knowing, though, I can say with certainty that you should avoid alcohol completely, as well as certain drugs/medications.
As Shelly said, it is important that you be followed by a physician, preferably a GI doc, for possible treatment.