Crystal, I am super sorry you had a bad day; I hope you know that everyone has days like that
Some other things to take away from your experience:
Make sure you know the date/time/place before you ever accept an order. If they don’t have the details, you can’t take the order.
I know you didn’t know the exact time of the delivery, but if the cake was still unfinished at noon on the delivery day, then there’s some time management issues going on. I’m sure every decorator is different, but I don’t go to bed on Friday until all my Saturday cakes are done. Sometimes that’s 4am.
Don’t get discouraged, but people ARE counting on you, whether that’s a birthday cake, a wedding cake, or a dessert table for a businesses’ photo shoot. There’s no real reason to be mad at them; they may have spent a lot of money to arrange the photo shoot and it sounds like by your own admission that you let them down.
I realize that I have rambled and not exactly answered your question about taking negative feedback. First, evaluate whether or not it’s deserved. If the shoe fits, do what you need to do to make it right, if there’s anything you can do. You will make people mad, and you will lose customers, but that’s no reason to hang up your apron.
I know sometimes people just want a hug and an “it’s OK” so I hope my candor doesn’t upset you, but I hope you learn from your experience.