Agree with Grog, Indogo and Mimi.

Sometimes, especially in times of no hope, what you want to hear is a voice from the cheering section. Nevermind about the cold hard fact. Mimi's comment is so spot on
I think you are brave and awesome. I don't know where you get the courage...
The question your sister asked was actually a cry for wanting support and not a question on whether to continue or not.

When you have a chance to talk to her and do it today is to tell her something like "I'm really sorry that you mis-understood me. Or maybe I didn't say the pretext of when I said no. I said in context of what if it was me. I'm just not as strong or as brave as you. So I am really sorry that it came out all wrong."

Just remeber, when you have a talk with her, she wasn't the one who mis-understood you. It was you who said it wrong. Take the fault yourself even if it wasn't the case. She's in lots of hurt and doesn't need any more guilt heaped on her. Sometimes, best support one can give is to take the blame, fault, or being the bad person. In the end, will it make you the bad person? no. Will you life change for the worse? no.

I'm dealing right now with my Alzeheimer father, with mother who just wants to complain and sister whos gone ... well... so it goes. And I'm the bad person, being the older sister and the responsible one. Yup I'm the meanie and the rotten heartless person. At least, my mother and sister can vent until they are satisfied and feel good.

I know you care very much and you are hurting too. That's why you are crying. We all do. I can truely sympethize with your hurt feeling and the anger. So dry the tears off, put yourself in your sister's shoes and think of what you are going to say. And think of what would make you feel better when you get a call from your sister.

Wish you lots of courage and patience,
Smilingcat