What you’ve described isn’t picky eating. It’s sugar addiction. Picky eaters dislike this and dislike that for a range of reasons, often because they’ve put their tastebuds in a state of arrested development frozen at a time in childhood when they tried x and didn’t like it and therefore will never try it again. You only want to eat sugar, period. That’s not because whatever cookies and sodas you crave are the only foodstuffs in the world you can tolerate. It’s because the enormous quantities of sugar cause your insulin to spike to reduce your blood glucose levels so you can survive the overdose, and then when your blood glucose levels crater, you are driven to replenish them.
I know it seems impossible to contemplate right now, but I think you have to cold turkey this. As long as you’re feeding the cycle, you are not going to lose all the weight you want and your cravings will never go away. Transition with sugar-free sodas if you have to. They’re not great for you either, but a Coke Zero once a day might help keep the habit at bay. If you’re anything like me, eventually you’ll lose the taste for that too.
Once you’ve got the sugar monkey off your back, your tastes will change, perhaps even dramatically. Keep an open mind. Set aside whatever hangups and presuppositions you’ve got about food and try new things. It’s a magical thing to find you suddenly love sour things when your whole life you’ve run the very sight of a dill pickle. That beautiful hit of astringence on the tongue is one of the great all time flavor experiences when you’ve spent decades under the spell of sweetness. That happened to me. I used to actuall get teary when a dill spear touched the side of my sandwich. I eat two garlic dill pickles a day now, and could probably eat a whole jar of them if left to my own devices.
Good luck!