My mom grounded me for something i didn't even do?

hi. ok, so at camp, my friend accidentally brushed her hand up against my neck. and since her nails were sharp, it gave me a cut. now it's all swollen and looks like a hickey. yesterday, my mom noticed it and asked if it was a hickey. i said no and told her the story, but she didn't believe me and grounded me for two weeks! i tried to tell her that she was wrong, but she wouldn't even let me explain. she was just like, "do you want to make it three weeks?" what should i do? this is so unfair! i had plans with my friends, and now i have to cancel them because of this unfair punishment! how can i get ungrounded?