AITAH? Had an argument and everyone is saying it’s my fault

So I was upstairs with my cousin who was going on to her mom about going to some coffee place. Her mom (my aunt) said she has to take shower so I suggested to my cousin lets ask my mom since I already have to go out to buy my cleanser we will go out to the coffee place too. We always go out with the driver at night but I have to ask my mom before that. We came downstairs and I asked my mom if both of us can go. She said okay. We came out of the room and I was going to ask our housekeeper to call the driver and take us both out. She was like she wont go now because it’s late (it was 9pm). I said we have been out at 9 before too so I was very shocked at her reaction. She was suddenly all paranoid about acid attacks and kidnapping and I was like who the hell is going to kidnap two girls in public place. And now that she said it my mom wasn’t letting me go either because in her eyes my cousin is the smartest person and I am the dumbest to ever exist. She told me to go with my dad but I was sick of my dad because he’s whining about spending money and my skincare all the time. I needed to use that cleanser because I have hypersensitive skin and cannot use any other chemical cleanser everyone use and my cleanser was completely empty. So I told my cousin Its all her fault and she refused to admit she did something wrong and even my mom was siding with her and yelling at me right in front of her and now both of them believe it’s my fault. AITAH?