Don't wear more then three colours, you'll look more put together that way. Try more muted colours rather then brights? E.g swap bright blue for navy. Even if you wear your usual style, you will look a bit more chic in muted colours that suit your complexion, without too much fake tan or heavy handed make up. Instead of skater dresses, maybe try a tighter skirt or shorts as you said-with a top with a collar/blouse? Collars make everything look smarter. Try a silky or sheer material rather then plain cotton/denim. Personally if i want to look smart then I wear all black with gold jewellery, but black can be draining on a different complexion. Of course I could be talking a load of balls and feel free to disregard me.
I would say go for black, navy or charcoal with gold or silver.
But bear in mind in my experience nothing makes you feel less comfortable/sophisticated than what I call the "grown up uniform" - something worn purely because it's what our idea of a sophisticated woman wears. I used to live in Surrey where it was like a uniform ... to the extent people would grill me about my lifestyle if I wore anything "alternative". So I tried the then uniform of boot cuts and a white shirt (aah tge early 00s) and felt a right fake. Way worse than not fitting in.