The challenge of avoiding the refined stuff
If you take to reading food labels you will start to notice some ingredients come up again and again. Sugar, MSG, high fructose corn syrup, spices that really don't mean "spices", things you can't pronounce. If you can't have it, chances are it's in that package you're holding.
White flour is pretty straight forward. If you can't eat it, that pretty much rules out all commercial baked goods--bread, buns, cookies, cakes, granola bars, even whole wheat items (because they usually contain a bit of whole wheat flour and a lot of white flour). With few exceptions if it was bought you can't eat it. You learn to make all your own baked goods from freshly ground whole wheat berries.
White sugar is a bit more subversive. According to the book Sugar Blues by William Duffy, Betty Crocker came out with a cookbook in the thirties or forties with the major purpose being to push sugar consumption. Apparently there was some sort of collaboration with the sugar interests of the day. That cookbook started calling for sugar (and lots of it) in dishes that weren't even supposed to be sweet. You'd add sugar to gravy and sauces meant to garnish meat! You'd sprinkle sugar over your meat and mix it into your carrot salad. Sugar made its way into all kinds of foods you don't think of as desserts, like salad dressing, mayonnaise, Ketchup, barbecue sauce, canned vegetables, spaghetti sauce, breakfast sausage, "healthy" breakfast cereals. In short, it's in just about everything that's in a package, jar or can and even in a few things that aren't.
You could spend hours reading labels at the grocery store, or just buy the whole foods from the meat, dairy and produce sections--your choice.
I try to buy foods that look more or less the same way they looked when they were harvested--whole apples, entire heads of lettuce, full cuts of meat with the bone still in. When I buy an apple, the only ingredient is the apple. Same with a bunch of radishes or a head of lettuce. Not all produce is entirely pure--many contain pesticide residues--but at least there aren't added ingredients like sugar!
My husband and I prepare the vast majority of our food from scratch and that's what you have to do if you are going to cut out refined flour and sugar from your diet.