How to deal with being rejected from Oxbridge with a sibling studying there?

I got rejected recently and my older sister currently goes to an Oxbridge uni (not specifying on the off chance she sees this lol). I've been trying to tentatively comfort myself (whilst feeling pretty pathetic about it) by reminding myself that the acceptance rate for her course meant she supposedly had double the chance of getting in compared to my chances, if acceptance rates even matter, and her course isn't something that a lot of people apply to in the first place. She was already amazing, and I had little doubt that she would be able to stand out amongst what is a smaller number of applicants in comparison to other courses.

But it's just sort of embarrassing? I'd never say this of anyone else, that getting rejected from Oxbridge makes you an embarrassment, but I'm very aware that my sister and I have always been similar. Our personalities, academic abilities, way of acting and talking - we've been matched in many ways since we were little, and in terms of grades I've sometimes even pulled ahead of her despite handling illness.

But at the same time, I've always felt like she's just been better than me, despite all the evidence that we're pretty evenly matched. I don't know if that's just a thing - that everyone feels like their older sisters are so much more mature, organised, disciplined. But getting rejected just really hammered down on my little inferiority complex in regards to her, and I feel bad mentioning it to anyone in real life because I don't want to make some crazy sibling drama out of my own failure and put a dampener on her deserved success.

Yeah, it's just embarrassing. I just feel weirdly ashamed and pathetic that we've always been similar, which was one of the reasons everyone else expected to see me get in, only for me to come out unsuccessful.