Telling your family is ultimately a personal decision up to you. However, it is a good idea to keep a list of all your current medications, history of allergies, history of medical conditions, history of prior surgeries, and list of all your doctors all in one place so that if you ever end up in an emergency room/hospital with altered mental status, a family member or friend can provide this information to the healthcare team taking care of you.
I suggest you consider telling your family wouldn't you want to know it it was one of them?
Really though for most people liver disease progresses very slowly especially if you don’t do other things to harm your liver like avoiding alcohol is a good one. I have had liver cirrhosis for 10 years caused by Hepatitis c and I am still mostly fine.
Having someone along with you at your appointment can help you remember what the doctor has said. You family member may also think of questions you did not.
You may want to write down a few questions for your doctor ahead of time so you don’t forget to ask. Also most of us with serious medical conditions keep copies of our lab tests and get copies of things like ultrasound reports so we can review them later as we try to understand our health better.
Sorry to hear you have gotten bad news but while liver disease is very serious with proper care you can live many more years by following your doctor’s recommendations.
Good luck