Diet as a verb is such a bad word. I had problems with anorexia and bulimia, basically the only way to get to a healthy weight is change your whole outlook on food, so small steps. You're not going to lose it all at once, so start small try and walk as much as you can and pledge to replace two unhealthy meals a week with healthy ones. Don't fall into the "I'm never going to eat this stuff again, so I'll have one more bad food day" trap, and don't try to just completely change the way you eat all at once. Have a clear goal on your ideal diet and exercise routine and make small changes every week to work toward those goals.
The shaky and weak business sounds like you might be eating too much processed stuff or too much sugar, and your body is now going through withdrawal. Are you getting headaches that last longer than a few hours, visual disturbances, any pain, weakness in limbs, heart palpitations?
If I get hungry between meals I grab some unsalted almonds or a piece of fruit. I've always got pretzels and fruit leather in my car to keep me away from grabbing fast food. I'm lazy as hell when it comes to cooking, so find stuff you can make fast or like raw if you're the same. Your plates should be about 40% protein (fish, chicken, lean meat, nuts, eggs, etc), 30% fat (cheese, avacado, walnuts, etc.), 30% carbs (fruit, veg, whole grains, etc.). I don't eat meat, only seafood, so my options are a bit less than most, but if you're interested in knowing more about that or what I eat on a given day, PM me.
I'm the same height as you, and I went from 150 to 223 lbs before. I got down to 139 from there thanks to rugby and not eating, and went back up to 190 because I stopped working out and was binge eating. I'm now a healthy post holiday 142, and have stayed within 5 lbs of that for a year and a half (although I'm losing weight from race training right now), but it took me about 8 months to get there. 128-158 is the ideal range for our height, but depending on your body type, you might feel and look great in the 160's, which is totally okay. Try tracking everything you eat, but watch the whole calorie counting thing so you don't relapse, focus on learning to eat healthy and watching your portions.
It's a beast to do, but you've already beat two demons, and it sounds like you're ready to start living happy and healthy, so I'm sure you can do it.