What diet should I go on to lose 15-20 lbs?

You should not worry about your weight. You're the perfect weight for your age. I'm 13 (almost 14), 5 feet 3 inches, and I'm 115 pounds. Perfect weight. You also shouldn't worry about what boys think about you. I have both guy friends and girl friends, and I don't care what my guy friends (and all other boys) think about me. Life isn't about getting someone to think you look "hot" or beautiful, or whatever. 1000-1600 calories is fine. Keep doing what you're doing now. Also, BMI is a load of crap. BMI calculators don't include your body shape, or muscle mass. I've used lots of different calculators, and one said 110 pounds is obese for a 13 year old (that was BEFORE I grew and gained 5 pounds).
Also, if your friends have BMIs below 20, they may need to gain a few pounds (depends on their age/current weight).
Hope this helped You are fine just the way you are

Some time ago, I read a book on losing weight that somewhat changed my life. I lost a lot of weight (for me) and have kept it off easily.

The book tells us to substitute food. For instance, instead of a typical desert of, say, pie, eat an apple instead. The apple is filling, contains only 80 calories, and is good for you. The book contains many other healthy and nonfattening foods that can substitute for all kinds of fattening and unhealthy food.

I found that I could get use to this substitution diet within only a couple of weeks.

I don't recall the book's title, but am sure that there are other books with the same advice.