Think of it this way, as long as you are working out relatively hard (but not hard enough to cause injury) your body will be turning fat into muscle. In terms of weight, muscle takes up a lot less space, so try not focus on the actual number of pounds you weigh, instead try to think of how healthy your body is as a whole (as you can weigh a lot and still have a healthy body).
Also, some people I have known have had some success in viewing their problem as a junk food addiction. They stopped eating junk food entirely (because saying things like "I've been good, I can have some junk food today" ended up being a slippery slope for them) and any time they felt a craving for it they instead ate a small helping of raw vegetables such as carrot sticks. They didn't hate plain carrot sticks, but they didn't really like them much either. The bland healthy snack food sort of made them want to stop eating sooner, and the caloric intake from vegetables is very small when compared to even a small helping of junk food.
It might be a good idea to talk to a nutritionist and/or a personal trainer so you can learn more and lose weight in the healthiest way possible.
Not sure if you will find this helpful, but I'll put it here anyway. A lot of people don't properly understand what hunger is. Hunger is your body anticipating food, it is not that you have run out of energy and need more. Your body anticipates food, and releases the insulin it will need ahead of time, which is part of what causes the sensation of hunger. Since most people eat at roughly the same times every day, the hunger will come at around the same times every day. With that said, you don't necessarily have to eat until you are full, but it is not healthy to skip meals entirely. You should eat if you get really hungry, but you should try to eat small healthy meals (ask a nutritionist for an idea of what that might be).
I have also found 'self-suggestion' very helpful in changing my eating habits, all of the things that are bad for me, I continually tell myself I don't like them (no matter how good they may taste), and I do the opposite for things that are healthy, but don't taste very good. Over time, I genuinely started to like the healthy foods, and started to find junk food much less appealing. Now that my body has adjusted to this new diet (which took me years to gradually implement) I find that fresh fruit tastes really sweet, whereas cake and the like are much too sweet and I don't like to eat it anymore.
Don't give up, you're doing well.