My endo suggested taking the beta-blocker before going to bed at night, I have just began taking Tapazole and Atenol, it has only been a week but I am feeling a slight bit better. See if taking it before bed helps, she also has me only taking half a pill, maybe talking to your doctor about the dosage will help.
Yes - we usually use beta blockers and tapazole together until the thyroid levels out then taper off the beta blocker. A lower dose of propanolol may work better for you -- ie 20-40mg, with the option of taking an additional 20mg as needed for high heart rate, etc.