OH MY GOSH! I am suffering reading about all this! I too am sending you my sympathy and good wishes. However, I am also the past victim of too much "do goodness". In fact, it helped me to become so very sick I think. I know I have had virus' and just doing too much did not give me chronic fatigue syndrome/fibromyalgia, but it sure didn't help.
Until I could learn to say no, and ask for help and look out for myself, I couldn't get any better. There was a time when I was nearly bed ridden. couldn't do much. Now I am able to go shopping, do household chores, join a couple groups, and enjoy a semi normal life at 69 with chronic health issues.
One thing I know for sure is that keeping to a routine really helps keep the dragon down a lot! If I even have my grandchildren over for a few hours or overnight, I am much more tired for days. And they are 11, 13, and 15! No real care needed. In fact, they can walk to Starbuck's and get me coffee!
The situation at your house is not good medicine for you, and you add that you help with the care of your dad. Whew! It is good and noble to aid a hurting family member, but everything I know says you need to set boundaries for your own health and sanity. I know how very hard it is for me when my adult step son visits, and he and my husband stay up late talking. Just loosing a little sleep is awful for my condition.
Your illness will benefit both by being a loving sister, and by helping your sister help HERSELF. I also know this from being a single parent and having to start over on my own with young children. It is hard, but it is good to learn how to go forth and do it. No one let me move in with them in my family. They listened, and helped with child care. No money was offered. I had to get strong and it has helped me ever since! God bless, and good luck. Mary