How quickly you can become addicted to a drug depends. There are too many factors involved to provide an easy answer. The biological make-up of your body, how sensitive you may be to a certain drug and the chemical make-up of the drug itself can all play a role in if or how quickly that you might become addicted.
If this is a concern for you please do talk with your Dr. Everyone here has their own unique make up so one answer will not fit everyone.
A drug you may want to discuss with your Dr. is BusPar for anxiety as it is not addicting and it works well for many people.
Be well,
Kitt