Will my anxiety really shoot up doing this or not because it doesn't do anything for them to begin with?
Firstly, beta-blockers should never be quit cold-turkey. As with many medications the body adjusts to their presence and a sudden discontinuation can cause serious physical consequences, more so with beta-blockers because of their affects on the cardiovascular system.
As for anxiety levels shooting up, this may happen though it won't be a direct effect of dropping the med. Beta-blockers, do not directly inhibit anxiety in the way antidepressants and benzodiazepines do and have little affect in the brain. Indeed, the water soluble ones which cannot penetrate the blood-brain-barrier are as effective for anxiety as the lipid soluble beta-blocks like Inderal which do.
Beta-blockers moderate the adrenaline surge that is part of the flight-or-fight response which is what really spooks people during an anxiety attack and often escalates anxiety. Discontinuing the med will remove that protective effect, but it won't in itself cause you to be more anxious, though it may prompt a, for wont of a better word, psychological increase in anxiety, as may any increase in pvcs and heart rate.
I'd really like to try to come off this medication but am so scared to even try! I'm afraid the pvc's will come back with a vengeance and that my heart rate will really become out of control. My doctor says since there isn't anything really wrong with my heart that I can get off these whenever I wanted to.
Your doctor is almost certainly right, but that alone doesn't help. Ordinarily, I would suggest that you taper off over only a few weeks, but given the potential for this to send your anxiety levels into orbit, your idea of weaning off very slowly may be the better option. From a purely physical angle you could reduce the dose every 2-3 days, but for you it would probably be better to just proceed at a pace you're comfortable with. You are unlikely to get into serious difficulty from any single small dose reduction.