I'm 17 and expected to take care of my dying grandmother. Am I being selfish if I feel like I shouldn't care for her alone?

No.

I doubt if your mother and sister mean care for her full time on a permanent basis, they might be talking about caring for her once in awhile with assistance from others. Do you ever care for her or help anyone else who's caring for her? Taking care of someone who's suffering with cancer is difficult, one person it doesn't matter how old shouldn't have the responsibility. If that's what your mother and sister are implying I don't blame you and completely disagree with them. The burden is far too extreme for someone as young as you.

A 17 year old should not be a primary caregiver. It is hard enough being an adult and a caregiver but there are many children who are caregivers.

A large number of children and adolescents are caregivers. They are truly the invisible caregivers. Nationwide, there are approximately 1.3 to 1.4 million child caregivers who are between the ages of 8 and 18. Most of them are not the primary caregiver. Hardly anyone thinks about children when they talk about caregivers. A lot of the children don't realize that they are caregivers. I was one of them. I helped my parents take care of my sick brother. My mother did most of the work but the entire family helped out. I needed to sleep in my brother's room to make sure he didn't stop breathing in the middle of the night. I never felt like I was abused. I just did it to help my family. I didn't know that other children were also helping their families. I wish someone thought about me when I was a child. 

Search AgingCare for youth caregivers. 

https://www.agingcare.com/articles/13-year-old-caregiver-essay-174237.htm

https://www.agingcare.com/articles/you-dont-know-what-you-dont-know-166638.htm

kellse, you're right. I recall a very similar post just recently.

do you go to school ??did you have to drop out b/c of this ..that is not right this will something you will pay for the rest of your life if you do not get the education you need you get back in school & tell all your family members if you have to !!!!! if you do not get a good education IT WILL BE HARD ON YOU !!!!! .UNLESS YOU ARE HOT & GET MARRIED TO A MILLIONAIRE BUT I DONT THINK SO SO GET EDUCATED YOU HEAR !!!!! IF YOU ARE IN SCHOOL & DO GOOD & SWING THE CARE GIVING THEN ID SAY MABE ..ALSO YOU HAVE THE FAMILY FOR REFERENCE FOR JOBS SINCE YOU DO THIS !!!!!!!!!!!!

Are you truly alone at all times? I had to help take care of grandmother in wheelchair (stroke) from age 15-22. My mother and caregivers mom hired took care of her too. I did not like it at all. I felt resentfulness and sometimes still do. You are obviously more mature than I was at 17 cos I would have never thot to ask anyone about it. Hence, I still get resentful over certain things. I felt mom was making me grow up too soon plus putting me in situations I wouldnt have chosen...like the caregiver who moved in w. us and felt she had to get involved in my life way too much...leaving me notes on everything...packing up my things and putting them on porch (like..."move") lecturing me, leaving bible verses etc accusing me of witchcraft and on and on. The caregiver also got involved with my closest male friend. None of the weird situations would have occurred had we not taken in grandmother. When all were out of town and it was just me and grandmother I always felt worthless as I could never measure up to moms standards of what she did when she was there. ..sleeping w grandmother, changing sheets four times a night...food preps...meds...helping her in and out of chair...constant bathroom breaks...doctoring of diabetic sores etc...too much for a 15-22 yr old ...then the worst was when she died in livingroom and mom in denial so I had to deal w 911, paramedics and making decision for them to try to resuscitate or not even tho she was clearly dead but my mom wouldnt accept so I made decision to try as I felt it would be best for mom to prove she had really passed. My chest is hurting and breathing labored thinking back as it all was nottttt a pretty sight. Id hate you to have to go thru any of it...but what can you do? Im just warning on the long haul as this stuff really affected me...like mom telling everyone how emotionally mentally physically exhausted she was for eight yrs and my teenage friends would say..."then why do it" but for me it felt a guilt trip...ie; why aint I helping more? Grandmother had lots wrong w. her and I felt ostracized by much...friends werent thrilled all the time. I felt I had to grow up quicker, get away immediately at 18. Even if I wasnt out of school. Mom even today will say that instead of her siblings taking grandmother, she did it cos they all had families. What was I? People always look strange at us about that. ...and she wonders why people wonder if we are related. Well...I have got off topic. Hopefully you will write again. I may be the older version of you. Id hate for you to feel years down the road the way I feel about that time of my life. Sending you love and hugs x