Me [16 F] with my sister [22 F] keeps asking me to babysit, and she's been getting mean about it, but I feel guilty saying no. She told me last Friday "what could YOU possible have to do on a Friday night??"

My sister and I were never close when I was younger. She was always a lot cooler than me and had a lot of friends and a great social life and she moved out when I was 11. We weren't close, I was always the lame younger sister.
My nephew spends a lot of time over at my house and I'm usually the one who takes care of him because the adults are busy and I try to engage him. I love him but I do get exhausted since he is here most days and he comes straight to my room and wants to spend the entire afternoon with me. I feel guilty if I don't step up and take care of him.
Anyway my sister started calling me up after she had a baby and I thought it was her maturing but a lot (or most) of the time it is to babysit, and I usually do. My nephew is 3 now. Last Friday I'd had a really stressful couple of weeks at school and had just finished my exams, and I was spending the night with my parents watching tv because I don't have any friends. So my sister messages me asking to babysit and I tell her I can't, that I'm busy. She gets all aggressive on me being like, what could you possibly have planned??? Was the general tone. So I got ****** at her and actually blocked her. It was a long conversation where she was basically insulting me the entire time. It was just a Friday and I didn't want to spend it on her couch, partly because she says she'll be home before 1am but she's always out until 4 or 5am at least.
She also started inviting me for dinner and I was really excited about it, she had two of her friends there too. Then at the end of the dinner she was like so we were thinking of going to see a movie! I was like awesome what movie! She starts telling me about the movie and I'm really into it and then she's like "so if you could stay behind and babysit that would be so great..." So I felt like the only reason she invited me was so they could go to the movies after. I felt like I was put on the spot and had to say yes because she'd just cooked me up a dinner. I mean that is a really nice thing to do. It'd be different if she'd told me beforehand? Or am I being a brat. This has happened twice now.
I don't feel good about the situation and I don't know what to do because I just end up feeling guilty if I don't help because she's a single mom and going through a hard time. What would you do?

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tl;dr: My sister gets kind of rude about expecting me to babysit but I feel too guilty about it to say anything because she's a single mom and because I love my nephew and I feel like I'm failing him if I don't step up, because a lot of the time other people aren't engaging him when he's over. What do I do?


Source.