Propranolol is a beta blocker most often precribed, until recently, for high blood pressure. It is slowly falling out of favor for that indication because there are newer drugs and it may increase the risk of developing type 2 diabetes.

It blocks beta receptors for the stress hormone adrenaline (epinephrin) thereby reducing the physical effects of anxiety's flight-or-fight response - the racing heart, clammy skin etc. While it readily penetrates the brain it has little if any effect there as there are no adrenaline receptors in the brain.

It is often prescribed to musicians and actors for performance anxiety.

Unless you have cardiovascular or lung disease, including asthma, propranolol is unlikely to cause any ill effects.

I suspect the tightness of the chest you experience is anxiety related and not a drug affect, but mention this to your health care provider at the next visit.