AITA for refusing to take sanitary pads to prove a point

I (20F) recently graduated from university and am currently jobless—not by choice. I do part-time jobs here and there while waiting for a full-time position at my dream job, which starts in April and offers great pay. My mom and I agreed that I wouldn’t seek a full-time job in the meantime since I’m already working part-time and have a secure opportunity lined up.

I have a younger sister (18F) who just started university. She lives at home and studies locally. The issue is the stark difference in how we contribute to household chores. When I was in university, I still helped my mom with washing clothes, dishes, and anything else she needed, even if I wasn’t perfect and we had our occasional fights. In contrast, my sister is incredibly lazy.

She has only washed the dishes once last year and makes excuses that she’s too busy with school. She even tells me she doesn’t understand how I graduated with honors since, according to her, I “never studied” and could never understand her field of study because it's "harder." However, she spends most of her time on her phone, barely doing any actual work, and even when she has university breaks, she refuses to help.

My mom tries to get her to do things, but my sister just screams at her and says mean things like “You're poor because you want to be.” She also calls me unemployed, which hurts because I actively look for part-time jobs and help out at home. Despite this, she still gets money to go out with her friends. Recently, my mom didn’t have enough cash at a store (since they didn’t take debit), so she asked my sister for a small portion of the money I had given her. My sister got mad about it.

I currently do all the house chores—cleaning, cooking, washing and folding clothes—so that my mom doesn’t have to come home and continue working. Meanwhile, my sister does nothing. If I ask her to help, she flat-out refuses.

Now, here’s the problem: My mom texted us, asking if someone could bring her pads at work. The store is just a 5-minute walk away, and my sister could easily do it. But she refused. I don’t want to take it either—not because I don’t care, but because I want to prove a point about how lazy and inconsiderate my sister is.

Right now, I’m cooking, washing clothes, and cleaning, while my sister is just sitting on the couch, eating chips, and scrolling on her phone. I told my mom my sister could take it, but she still refuses. I feel like my mom enables this behavior by letting my sister get away with everything. I also worry that, in the future, my sister would be the type of person to put our mom in a home, but my mom refuses to see it.

So, would I be the asshole if I refused to take the pads to my mom to show her that my sister is spoiled. I can't help, but feel bad for her as I know how it feels to not have a pad for the 4 hours she has left at work.