Hmmm ... I think soreness is the least of your problem.
You can't stop eating chips because they're good, but you don't eat meat, and you won't eat breakfast because it'll make you fat? You may or may not have an eating disorder (that's not anything I'm qualified to diagnose) but you do have some really bizarre ideas about eating, apparently.
Food is probably 80% of the battle in losing weight. Don't get me wrong, exercise is important, not just for weight loss, but for other health reasons as well, but you can exercise until you fall over and if you're eating a bunch of calorie heavy junk, then you're not going to lose weight, plain and simple.
You need to eat breakfast. You need to eat a reasonable amount of calories (at your weight, that's probably around 1600-1800 calories) of HEALTHY FOOD. I cannot stress that strongly enough. You're a teenager and right now is when your bones, muscles, and organs are developing - which will influence the way your body behaves the entire rest of your life. If you don't nourish yourself properly NOW, then 10 years from now when you want to lose weight, it'll be that much harder because you'll have damaged your body by not eating well.
Ok, that's the nutrition lecture over with.
Exercise: You say you've developed your own plan? What is it, exactly, and where did you get the information to develop it? Is it a healthy, sustainable plan? Is it something that you can do safely? Give us more information so we can help here.
Now, to your specific question: as far as being sore, yeah, if you are normally inactive and you start working out, you're probably going to be sore. If you overwork yourself from the beginning, you're going to be VERY sore - and I hate to be the bearer of bad news, but the soreness is generally worse the 2nd day. It's called DOMS (delayed onset muscle soreness) and it's very normal when you work your muscles.
The best thing to do for it is to keep moving - take a warm bath, take some painkillers (ibuprofen is best), do some gentle stretching or massage, take a long walk ... anything to keep the blood circulating to the muscles and help them to repair themselves more quickly.
And maybe think about EASING into a plan of healthy eating and exercise, rather than killing yourself the first day.
