How do I get out of my overly vain 'trophy' mindset when it comes to universities?
Since nobody seems to answer this somewhat vague question, I will:

1) Your question is not related to Academia directly, it is simply a question about fighting negative emotions (perhaps, jealousy?) that stem from failure in some sort of a competition. You say your negative emotions interfere with your everyday functionality, so the standard advice is to go to personal psychological counseling.

2) The one bit that is related to academia is:
"One of my friends got into Oxbridge and I don't think he's more intelligent than me or particularly gifted at all to be honest, -but I just don't understand?"

The answer to this is that academia is not an intelligence contest. It doesn't matter at all whether someone is intelligent or dumb. What matters is, for better or worse, whether you can deliver good research results.