If you can sympathize with your daughter's percieved "need" for those deliberately attractive consumer goods, give her some choice, and be clear before leaving the house what the rules and consequences are, you'll be able to move your daughter past this behavior quickly.
Just as with any major area of modern life, children need to be informed about what reasonable limits are. My Grandboy 4.5 has discovered his Inner Consumer, and begs for nearly every appealing thing he sees when shopping. When she was little, my daughter did it, too.
It's what all kids do when they realize stores are a place we can satisfy our materialistic urges – but they will only do this to the extent that they are allowed. When they learn that whining or screaming doesn't bear fruit, they will stop. But for most red-blooded kids, it does require parents to hold a firm line when that initial experimental whining starts. If they don't stop it then, it can (and does!) evolve into full tantrums.
Now that you've given in a few times, you've intensified a completely normal dynamic. Please don't punish your daughter for being "extremely spoiled." She's doing what comes naturally, so you need to reset HER expectations.
I've done a few things to set out my limits and expectations BEFORE a trip to the store. First, I acknowledge that there will be things my grandson wants, and I empathize. Yes, those treats will look SO good. Yes, the bakery section has such beautiful cupcakes and cookies. Yes, the toy aisle is full of things kids like to play with. Yes, when I go to the store, I want things I can't buy, too. Oh, well.
I also give him the information that my funds are limited. Often, kids have no idea at all that their mom or granny doesn't have endless cash.
I gave my daughter a nominal amount of money before trips, an allowance of sorts, starting at about 4 years. I actually set this up so that she got to choose to opt in; her choices were a treat that she could afford, or no treat at all. Of course, she opted in. So, I told her what things this ($) would purchase, and told her she was free to buy those items, or to save the money toward a bigger treat in the future. I pointed out that she had the freedom to budget, just like big people, who only had enough money for the week's food, and had to decide what they could and could not buy.
I also told her that if she started begging, she would have to wait until the next trip to choose her treat, and try again. As she gained experience, I also pointed out that deferring a treat this trip would give her twice the working capital the next time. I'd told her I'd remind her only twice if she started begging, and then her chances to buy a treat for that trip would be done. During the shopping trip, I might whisper to her, "Now, what did we agree about begging, sweetheart? Do you want to choose yourself a treat, or will we have to leave with no treat for you?"
While I never had to do this, I was fully prepared to abort a shopping trip if her behavior became unacceptable. Some kids will have a harder time getting the concept of limits. It's temperamental, and they can't help it. For such children, I would do what other moms have suggested – one or a few trips focused not on a successful trip for mom, but a training trip for the child. If you have the freedom to leave the store without sacrificing tonight's dinner, you'll have a much easier time staying calm and in control if your child starts acting up.