You are sixteen years old! you have your whole life ahead of you, the sooner you embrace recovery the better, and you will be so proud of yourself when you get your period back and when you can do sports again, because you'll have your life back. It's not too late, it would be tragic to throw away your teenage years now and spend them in treatment centres.
What's more important? a number on the scale or a life without worries over food, the chance to have babies, enjoying food again!
It's scary, and it's going to be really hard, but it get's easier, once you start gaining you'll see how wonderful food can be and you'll relax a lot more, once you get more curves you'll start to look healthier and softer and much prettier i assure you :)
As for meals.. this is just a basic idea of a 2500calorie plan, you might need more depending on your stats etc
Breakfast: Bowl of wholegrain cereal with full fat milk, 2 pieces of toast spread with butter/peanut butter, a glass of fruit juice
Snack: Lara bar? clif bar? any kind of calorie dense bar really
Lunch: 2 thick slices of bread spread with butter and filled with whatever you like (cheese/ham/peanut butter) a piece of fruit, a glass of milk
Snack: Big hanfull of dried fruit and nuts
Dinner: Protein (chicken,lamb,pork,fish) some sort of carb and it must be a decent sized portion! (Pasta,rice,noodles,large baked potato) and loads of vegetables (don't worry about quantity!) also have another glass of fruit juice
Dessert: Challenge yourself every day to a dessert you love, don't worry if you can't have a full serving to begin with, but then again, don't worry if you start having two servings!
Snack: try and have a milky drink before bed (hot chocolate,milk,horlicks) and a couple of biscuits if you can manage it!
What you eat can have a direct effect on your skin if you're struggling with psoriasis. See what to shop for.