AITAH for blowing up on my mom and sister

One day I was out with my girlfriend who lives about an hour away. I usually only see her twice a week because of how our schedules work, anyways I was invited to a pow wow my girlfriend and her family were a part of. As I was there I also decided, why not do a school project as a piece for my critique that was due in a few days. So I took my requested day off to spend time with my girlfriend as well as a productive time to do my class project. Well in the middle of the pow wow I get a call from my sister saying that my mom needs help pushing (my sister’s car) onto a U-Haul trailer to get it towed to a mechanic shop. I said I couldn’t because I was an hour away and I had plans, but I did offer the fact that I have friends from a car club I am a part of that I can send to go help. My sister then proceeds to tell me that my mom wouldn’t feel safe because she doesn’t know these people. And if that was the case I would have to pay for my sisters tow to the mechanic shop. So I went ballistic because how is it my fault when I offered help in a different way. I cussed my sister out and told her it wasn’t my responsibility to help her get her things situated and it was called being an adult .

Backstory: my sister travels about 2 and a half hours every couple times to visit my mom, but she doesn’t take care of her car such as checking fluids ,tire pressure, basically just proper maintenance, well this time she went over about 3,000 miles on her oil change and low and behold her car threw a rod because she had no oil in the car and she drives a Hyundai. Well when that happened I went to go help her the next day to help diagnose her problem instead of her getting charged a diagnostic fee from a mechanic. And one time my moms alternator stopped working and I called out my next work shift to go drive 2 and a half hours to fix the alternator on my moms suv. Reason why I say all this is because after yelling at my sister my mom tried to guilt trip me and say “ I know who not to call in case of an emergency.” Like bro !? What!? I’ve helped them countless times but it seems if I can’t do it one time it’s like I never helped them out at all. So am I the asshole ?