Can my nose shape change in my puberty stage? Should I get a surgery?

Unlikely.  From the onset of menstruation until about age 16 for young women the nose will have ahchieved its size and shape. With age things will change but  unlikely for the better. 

At age 19, the nose has finished growing and it is acceptable to undergo a rhinoplasty procedure. Rhinoplasty is a difficult endeavor, such as your surgeon very wisely based on extensive experience

Rhinoplasty is a surgery to improve the shape of the nose for breathing or appearance.The nose grows along with the rest of your body. The facial bones surrounding the nose grow through puberty. It's considered safe to perform rhinoplasty once your bones have stopped growing. A good indicator that your bones have stopped significant growth is when your shoe size stops changing. Throughout your life, your nose will age along with your body, but these changes should be slow and subtle.  Consult with a surgeon to determine what options would be appropriate for your face to produce a safe and lasting result. Safety comes first. 

A young lady's nose is fully grown by age 19 so you could do a have a rhinoplasty at any time. Consult with a rhinoplasty specialist so you achieve a natural result.