If you are otherwise healthy, I wouldn't worry about it. There is less social pressure for women when it comes to height and stature.
So, I would just focus on being as healthy as possible as the primary focus rather than focusing on how tall I am.
By the way, I'm just barely within range of what is referred to as average height myself. When I was your age I was as tall as I was going to get. If it's in your genetics, you might get a final growth spurt in a couple of years. But, if this is not common for women in your family, don't expect it. Otherwise you'll set yourself up for disappointment. So, yes, I'm taller than you, but I'm still on the short side. I still have to ask for help if I'm at a grocery store and the item I want is way up there on the highest shelf.
In other words, accept yourself at whichever size you come in. Have you ever heard the expression: "Good things often come in small packages."? Who you are inside is far more important. If you let your happiness and your self acceptance show on the outside, you will attract the kind of people you want to be with. Another expression that fits this: "You'll attract more flies with honey than with vinegar."
Self-acceptance is the key to all aspects of life, but we're often very sensitive during the teenage years. So, when the adults are telling you to accept yourself at any size and show who you are on the inside, adults are speaking from experience and truly only trying to help you have a good life.
Your height is below the 5th percentile for your age, however, you are 16 and may grow some more for a few more years. If there are women in your family that have a small stature, then it maybe genetic. Eating healthy will help you grow. You need approximately 2000 calories per day for your age/height. Fruits 2cups, Vegetables 2.5 cups, Starches/Grains 6ozs equivalents, Meat & beans 5.5oz, Milk products 3cups, oils (unsaturated) 6 tsp and discretionary calories 267. Fluids are 8 cups a day or more depending on how much you exercise, etc. All the above food needs to be spread between 3 meals and snacks between meals. Hoped this helped you.