1st, I hope you're seeing a therapist and also, preferably, a dietician. Folks will give you the best advice they can, but most people don't really know how to deal with both fitness and emotional health. As a former 360lb man & and still struggling binge eater, I can tell you that the advice of someone who isn't trained or hasn't dealt with this stuff personally has as much potential to do damage as good.
Reminder, weight gain and loss are something that occur over time. One 2000 calorie meal a week doesn't kill my diet, as long as I take it in context with all the rest of my eating and fitness habits and adjust them to account for the extra intake. You don't need to burn those calories off today. Learning peace, patience, and an ability to give yourself grace should reduce the anxiety, and, in turn, the desire to binge.
Let those specialists and your support network help you.
Try Yoga. It helps with your sleeping disorder and reduces anxiety. I am talking from my experience. It will gradually reduce your food intake too. All the best.
Set a routine. On Sundays pack you meals in Tupperware. Portion control breakfast lunch and dinner small snacks between meals. And workout when you can I do an hour workout every night