My mom was diagnosed with cancer 7yrs ago, when she could no longer care for herself and my sister with Down-syndrome properly I moved both of them in with me. For 2yrs I was the sole person taking my sister to her Dr's appointments because my mom had become to weak to do anything but make it to dialysis. Before I moved them in with me my sister health care had been put on the back burner due to my mom's condition, so I had no idea of the care that she also needed, but was learning all that was going on with her while trying to care for mom too. My mom passed 2yrs ago and with new problems arising for my sister I am having problems getting Dr's to see her because I am not the legal guardian or have POA. Fortunately I am not having problems with her primary or any of the Dr's that knew about my mom's condition because they knew that I would be bringing my sister to the appointment because my mom was ill. But when they refer her to another Dr. or specialist, that's when I have problems. They will not see her unless I have documentation.
If sister can't understand the concept, then I think your only recourse is court intervention to give you authority to act for her.
Others here can speak from experience with that.
You must be a very special person to take this on. Are you taking care of yourself, too? Are you getting any help in caring for your Sister?