Well good luck with it but if you succeed, it sounds like nothing could stop you in life!
I mean how are you going to lose weight when your appetite is through the roof? I can't imagine how that could work.
But as for exercise, normally, i'd say you don't need to exercise much to lose weight. Some say the ratio should be 20% exercise and 80% diet anyway. Certainly you don't' need the kind of exercise like going to the gym and stuff. Just be active in your daily life as much as you are able.
Maybe the key will be other features like what you eat - proteins v carbs v fats, and how much you eat. i.e. not too low calories and no crap processed food. I think i've just learned that protein helps with craving avoidance and things of that kind. I should read the article again. (see Insulin on nutrition world if interested)
If you make a concerted effort to quit all the crap foods, and eat high fibre, especially soluble fibre, and the rest in the usual recommended balance of macro nutrients, you will have the best chance i think, given your medication issue. I mean given you may want to eat a lot, the foods you want to eat a lot of should be low calories, high satiety stuff. I hope you know what i'm talking about.
btw this time one of the things i am doing is making managing my stress a priority in my diet and not letting stress/depression/etc ruin it for me. the other night i had to binge on carrots until i decided i could pinch a bottle of my father's wine. A glass of that resolved my binge and enabled me to go to sleep. no regrets the next day.