If you only have PVCs (benign) and short runs of SVT there is no reason not to exercise.
The fact is that if the SVT occurs and persists for more than ten or fifteen minutes then you need to get to the ER to get it stopped, but at your age this is more of an inconvenience than a danger.
If the SVT becomes a recurrent problems you will need a cardiologist to determine if you can have a procedure called an 'ablation' (not surgery, done by catheterization of the heart) to fix this permanently.
But, for now, there is no reason not to increase your exercise and fitness level. Touching base with your cardiologist would, of course, be beneficial.
The propranolol should be protective so please do take it.
Also, if you have not had your thyroid function checked this would be prudent, as overactive thyroid can cause tachycardia (fast heart rate) and this would be an important thing to rule-out in your evaluation.
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