Hi op, it sounds like you have a big confidence issue. And that's affecting everything.
Many people have weird accents (me included), I'm not from an english speaking country but because I'm fluent and sound like an english speaker I get asked if I'm feom Scotland/ireland/America etc. I don't take it as a criticism, just a point of conversation.
If I had a speech impediment, that's what I would say I had. No biggie.
I never think that people aren't going to like me. Not in an arrogant way but because I am a nice person so presume people like nice people. And when I meet people I always start on the basis that I'm going to like them. I think that is normal.
You sound really lovely. People will definitely like you.
In terms of things that you're conscious of (you're probably being overly critical) but there are so many things that you can do nowadays. My friend has really thin hair which never grows as long as she would like so she wears extensions.
If you really dislike your nose (I don't like mine either, I think it is too big, but when I've pointed it out to friends they say I have a nice nose (I'd much rather have theirs)) you can have rhinoplasty. Or go to a make up person who can show you how to highlight the bits you want etc.
And yes, join clubs, sports, hobbies, activist movements, whatever you're interested in and get to know like minded people and enjoy your life :)