Losing weight as a picky eater is a tough proposition, but it's definitely not impossible. You can continue to eat some of your favorite foods and not have to shove those dreaded vegetables down your throat. Obviously, working to add healthier foods into your diet would help, but you need to get on track for weight loss before worrying about that.
The first step is finding your motivation for losing weight. Don't jump into a dieting plan without figuring out why you want to lose weight. Just wanting to drop a few pounds won't be enough motivation for most people, so pick a goal that will make you stick to this diet. If you're having trouble thinking of something, here are a few examples: