There is no 100% accurate answer to whether or not you will grow any more. Doctors do their best to predict when you will stop growing, but there are always exceptions to the "rules" that they use. It is true that your adult height is influenced by a number of factors, mostly how tall your family is and whether you are a boy or a girl. But, there is also a significant input from the environment, including nutrition, exercise, and any underlying health problems you may have. In general, most girls do stop growing about 2 years after they get their first period, but there are a few who still grow a little even in their teens.
TeenHealthFX wants to reassure you that you are not "short." Perhaps because your family is so tall you feel this way, but 5'6" is above average for females and is a completely normal height for you. One method that doctors sometimes use to calculate height is adding together parents' heights, dividing by two, and then subtracting three inches for a girl (or adding three for a boy). However, it is important to realize that the child's ultimate height can vary by as much as five inches above or below this calculation. So, even at 5'6", you are completely within this range based on your parents' heights.