Beta blockers can be tricky! Dosing is actually the tricky part. Too high of a dose will make you "sluggish".
Beta Blockers are commonly prescribed for anxiety. In fact, the most common use outside of cardiac issues is for stage freight.
As far as you becomming "addicted", i can try to address that. Beta receptors are located on the heart and in the lungs, among other areas. You've got these receptors that are use to having things like epi (speeds up heart) attach to them. The thought with anxious ppl is stop the natural heart racing biomediators from attaching and their heart rates slow, and the beat is less felt. Doctors give Beta Blockers (Adrenergic Agonists) (adrenergic=fast heart, dilated pupils, slowed GI...etc) to reserve the receptors so that those other caffeine like stimulants cant park there. Problem is that the receptors are wondering where the heck the epi and that "rush" is and the cells in response make more receptors than normal. All fine and dandy while you're taking you're "blockers". Should you abruptly stop, you'll have all these empty receptors, a heck of a lot more than usual, no blockers .....Epi has a field day. Overstimulation, severe tachycardia, severe angina (chest pain)....An overall SPEED response that can lead to MI (heart attack).
I would worry more about "addiction" with benzo's, opiates, sedatives, etc.
Woo hoo! Somebody just had a pharmacology test

And somebody has been on BB for a while