Op 
I think you would benefit from CBT, it's really good for overcoming unhelpful thoughts.
The company you work for sounds sterile and hugely corporate I can guarantee you that you are not the only person who feels 'odd' or 'wrong', it's not a very humane environment is it?
My suggestion would be:
CBT asap, even a few sessions and reading a book about if will hopefully shift some of your negative self image.
Book yourself in for a personals hopping at JL or ask a very good friend who is good with clothes and who genuinely cares for you to give some feedback or tips.
Try and do your very best in your current job but try and listen to yourself too. Maybe you are having a burn out without knowing it yet. Get some rest, decent sleep and bait of exercise. It doesn't have to be a huge fitness regime just ale one or two changes every few days.
Consider changing your industry and bringing your wonderful talent to the charity sector.
Take a sabbatical (if possible, may not be).
Be kind to yourself, don't try to be perfect, you a living breathing human being and perfect as you --as hard as that may be to believe in the corporate environment you are in.