When we give out more than we get back for any length of time, the person we are giving to is a taker. This is a guaranteed drain on your well-being and there is no end if you keep giving to her. Technically this type of giving is called “enabling” because is actually enables the person you are trying to help stay the way they are. Your sister hasn’t adequately grown up — and a large part of this as you have rightly determined is that you are enabling her to remain as she is. It doesn’t matter if she is playing mind games with you or not. What we know for certain is that she is a taker.
The 12-step program Al-Anon has offered help to those individuals who are family and friends to people who struggle with alcoholism. Much of what they promote for their members is detaching with love. I think this is a good suggestion but have found it can be enhanced if people are given the task of detaching with compassion. I believe is necessary here. I think having compassion for your sister while staying unhooked from her is the right thing. You have to live your own life without this constant thankless drain from her.
The difficulty in doing this has to do with the guilt people usually feel when they stop supporting (enabling) their loved one. But the guilt is something you can manage whereas the resentment you’ll feel by getting roped into her shenanigans has become toxic. I’d be blunt with her and not mince words. Let her know that it is too much to continue and that you now need to take better care of yourself. This can include informing her (and perhaps yourself) to find a support group either online or in person. Here is our comprehensive list from PsychCentral for these groups.
Finally, I highly recommend that as you do this you develop some self-compassion for your self. There is an exercise here that I’ve developed for my forthcoming book Learned Hopefulness, that you can find on the bottom of the page. I’ll encourage you to develop these supportive feelings for yourself as you detach with compassion from your sister.