The only way to get taller after having stopped growing naturally is to get surgery, however, I believe your doctor is a little mistaken about you ending up short. Google "Does menstruation age affect height" and there will be tons of results that tell you no, and some that say that early menarche means that you will grow taller than those who start later.
I got my period at age 11, and I can tell you that I definitely wasn't 5'5 at that age. So depending on how old you are, you probably have at least a few inches left to grow. Don't fuss too much about it, and if you do end up short you could always wear some shoes that make you look taller.
Tbh, the younger generation these days tend to be taller then their parents, maybe something in the food we now eat.
13 is very young for your doctor to tell you that your height is leveling off. You have many years to grow. Judging by how you describe your brothers height - my guess is that your will follow suit. Maybe not as tall as your dad but not far off. and like another has said, not much you can do with out surgery - your young, dont worry about these things, just keep active and eat good food :D
Dieting excessively is a surefire way to stunt growth - eat enough, eat healthy foods, and exercise and let your body do its thing.