Is it possible for a girl to still grow to age 17?

Varies among girls: Most people reach their maximum height in their late teens. Without nutritional problems or chronic childhood illnesses, height is largely based on genetics and parental heights. Aside from eating right, exercising, sleeping well, and being happy, there's not much a person nor her doctor can do to affect height. So, the general answer is: yes, it is possible.

Yes: At 14 you have reached most of your adult height, but you can still continue growing up to about age 17. In any individual, linear growth (height) stops when the growth plates at the ends of your bones close.