Amelie, welcome aboard!

If you ask me, beauty is something that radiates from within. I don't give a hoot about external looks, as it's the beauty within that really matters in the end.
In my humble opinion, doing a nose job for the wrong reasons (such as appearing more physically attractive to a prospective partner) will probably get you the wrong person. Well, actually, maybe for you it would be the right person. Here's what I mean: you'll attract a guy who appreciates you for your external beauty. If that's what you want, fine. But if what you want is a partner who values you for your internal beauty, you'll attract such a person without having to go through the nose job.
I used to be so socially inept, so I can relate to some of your social difficulties. I've found that being in therapy, where I was actually taken seriously, where someone had a genuine interest in me and my internal and external life, it boosted my self-esteem. Not to mention all the work we did through the years. Still, the relationship with my T was therapeutic in itself. So perhaps you'd consider a trial of therapy.

Wishing you the best of luck!
Take good care,