In general, female breasts stop developing at around 18 or 19 years old. This is when a primary level of maturity is achieved, however further changes occur with pregnancy and lactation (the production of breast milk). Your breasts will continue to change throughout your life, as the signs of aging become more apparent. For example, your breasts may begin to droop as supportive tissues weaken, or grow larger when you gain weight.
Women's breast can develop until their early twenties. Having said that, breast size is genetically tied. If your female relatives have smaller breast, you may not get any larger. There is no way for a doctor to predict how much larger you will get I am afraid, so it is a matter of comparing yourself to your relatives and waiting I am afraid.