18 years old and scared of older cousin

I’m just barely an adult, just made 18 and I live with my parents so I don’t have an option of saying no. My aunt called and told me to pick up something from her house for my mom this afternoon when I get out of school. I will be picking it up from my cousin who I do not like or interact with at all. This cousin made fun of my teeth (I have an overbite) and it’s a huge insecurity of mine. She did it in front of my mom who said nothing, her mom who also said nothing and a bunch of other people who are friends with her mom. I tried to defend myself but my mom told me I could not. This cousin is 15 years older than I am so I did expect someone to intervene being that I was not allowed at the time due to my being a child but no one said a word to her. They did try to console me afterwards but I was humiliated. I do not want to go to pick the item up and I tried calling my mom about it but she is avoiding my calls because she doesn’t want to interact with my cousin either as they don’t get along very well and it always ends up in an argument. I don’t know what to do but I really don’t want to go over there and pick it up and it’s not something that’s important it’s just something my mom doesn’t want to pick up and my cousin doesn’t want to drop off.