You answered all your own questions. Diets never work. Starving yourself only makes your metabolism worse and makes you bigger, not smaller, and binging just makes that metabolism factor even worse!
With what you're going through, Testosterone would only make it worse. Right now I feel hungry 24/7. However, I eat small meals 5 times a day and I have absolutely no junk in my house. Never have it. Nothing for me to snack on but fruits, yoghurt or veg.
The reason you're not losing weight is because you're doing pretty much everything wrong, and that's okay, it's what we think will work but never does, it's counterproductive. If you don't see results, and you miss food you love, then you fail! It's a predictable failure so you can't blame yourself really, the way it seems right to go about it just sets you up for failure as inevitable.
The successful route: start eating 5 times a day at regular intervals around 3-3.5hrs. And schedule moderate exercise daily. Go for the daily 30. Cleaning your house counts as exercise. Walking on the spot while watching TV counts, just get 30 minutes of moderate exercise going EVERY day. Then add in any workouts on top of that if you want to lose more at a faster rate. The benefit of exercise is increased drive, energy and motivation (which helps you commit to making all those small meals lol). Exercises for losing weight are exercises that combine cardio and weights. Muscle increases metabolism and cardio speeds up the fat burning.
And most importantly schedule treats or you will absolutely and positively fail. Anyone trying to go for a healthy eating plan by thinking they'll never touch their favourite foods or sweets again, I'll tell you right now, it's not even worth starting. They will fail outright. I said I don't keep junk in my house, but I have days where I schedule to make myself a burger, or pizza, or buy a little chocolate for myself; whatever I enjoy. Then you don't look at eating bad food as a "slip up" or outright fail. It's just a treat you deserve!