Give her more choices and pick your battles. Instead of telling her what to wear either let her pick anything out or you choose to outfits and let her choose which one. As to shoes, let her wear what she wants. This is a battle I would not choose to fight. Really, what does it matter that she's worn them everyday this week?
What is scary about her behavior? She sounds normal to me. She just needs to have more control over the things you mentioned.
As to not obeying in public. If you tell her to stand in line with you and she doesn't, then go to her and hold her hand while you bring her back to the line. If she fights you, take her out to the car to sit until she's able to say she'll stay with you. Is it that sort of thing?
At 6, I would get her input about what clothes to buy but the decision to actually buy it would be mine. She may like it in the store but find it's uncomfortable to wear. It's too much responsibility to expect her to wear something just because she chose it at the store.
She may just want to wear something different on this day and will wear your choice a different day. Again, give her choices everyday. Let her be in charge of as many things as possible. Short term choices. To choose to buy something last month and expect her to then wear it today because she chose it last month just isn't reasonable.
Also, try to think how she might feel in this situation. Would you wear what someone else chose for you everyday? You bought an outfit last month and would you wear it today because you chose it last month or would you wear what you felt like wearing today?
We give kids choices, based on their maturity, so that they will learn how to make choices. You chose her clothes for you when she was a toddler. A toddler doesn't know about the weather or the factors that go into making the choice. At 6, she needs to learn how to make the simple choice of what to wear so that she has practice making choices. The consequences of a poor choice in clothes is minor. Perhaps she'll be cold when she chooses to wear shorts and a t-shirt. She'll know better next time if you don't turn it into a battle.
By having consequences for her choices she will learn how to make better choices. Start with the choices that have minor but safe consequences so that she'll make good choices when she's older and the choices are more serious.