Yes you can easily become dependent on xanax, and when you wean yourself, do it very slowly. Xanax is also depressing, so even though it helps with the anxiety symptom, it does have other undesirable effects.
Since tightness in your chest is an anxiety symptoms, you would be much better off learning how to quiet your mind through your own mental awareness and understanding than having to depend on drugs for the rest of your life. You can learn this by exploring meditation, cognitive therapy or visualization techniques.
I work with clients daily that are in trouble with benzodiazepine medications.
Raz