You are at good age to start ballroom. Although many professionals start at age 6-7, just as many start in their teens. It is possible to start even as an adult and reach a very high level, but not the world-class level. Just to give you an idea, it takes about 6-7 years to become really good in ballroom if you train with good teachers and don't waste any time. So if you start now you will be a good dancer when you are 19-20.
Those who start in their 20s and later tend to stay amateur forever or turn into social ballroom teachers which is not the same as competing professionals.