Hello. Welcome to PC. I'm sorry you are having a tough time. You need to set some healthy boundaries and have consequences if they are crossed. Stick to them. Like you telling your sister that you would not be paying her fees unless she got a job. That's great. You just have to stick to it. Your sister's behavior is outrageous.
You could also determine what you are willing to contribute financially for the sake of the household and let your family know what it is. Also parse out the chores. For you to be working so hard and having nothing left for yourself is just wrong. You may end up having to move out to have a life of your own. Good luck in reaching a satisfactory resolution. Sending big hugs.