First off I should say that I'm a vegan. Secondly I have braces and have to get the wiring and bands replaces every two months. It really hurts and tends to hurt for about a week or two. I need really soft, but nutrient filled, foods that I don't have to chew for the time that I can't eat normally.
I'm in the same boat as far as the braces and adjustments go...but I'm not vegan. So, a lot of the foods I eat won't work for you (omelettes, scrambled eggs, certain soft meats such as salmon, etc.). I imagine even yoghurt and cottage cheese are out in your case too, given the restriction against dairy...correct?
I also eat soups, and there would be some soups (vegetable, etc.) that would work for you, plus protein shakes and smoothies. I also find that, after the first couple of days, I can eat a salad, as long as there's nothing too crunchy in it.
All that said, my calorie count goes way down right after my adjustments, since it is quite painful to eat anything for the first few days.
I make a vegetable soup in the blender with a brick of tofu, 1 cup broth, seasonings, and either a small container mushrooms, a box of thawed frozen spinach, a jar of roasted red peppers, a few zucchini, or whatever sounds good to you. I have a Vitamix, which blends and heats, but if you don't, you could cook on the stove and then blend with a stick blender.
I really liked mashed potatoes...you can add a bunch of different seasonings to mix it up a little. Smoothies are great too, and you could buy some protein shakes
Oooh...speaking of mashed potatoes...how about shephard's pie? My daughter is a vegetarian and I know she makes shephard's pie with lentils rather than ground beef. That would be nice and soft when your teeth hurt.