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Add some more beans and legumes into your diet. Have snacks in between meals of as much fruits and veggies as you want. That should help you feel full. Is it possible to eat peanut butter with braces? If you can eat that or almond butter/cashew butter/soy nut butter that might help.

For a good source of nutrition info try the book Becoming Vegetarian (there is also one called Becoming Vegan if you end up going vegan). It has all the info you need to make a healthy diet. I've seen it at the library as well as used book stores if money is an issue. In Becoming Vegan there are meal plans for different calorie needs. I imagine that's in the vegetarian one too.

Good luck. With a little tweaking you will find out how to get enough to eat so you don't feel hungry. The nice thing is that many things you eat as a vegetarian don't have to be limited (fruits, veggies, etc.) so you can eat as much as you want of those!