Why don't you ask your pharmacist or doctor because it may not be related and there may be something else causing it that she can give advice on? No one here can diagnose you and might steer you the wrong way with anecdotal evidence that might be wrong.
I have booked an appointment with my doctor, but my usual doctor I see, who knows about my struggle with anxiety and prescribed me the propranolol is out of office until Monday (4 days from now) I have booked an appointment to see her on Monday but I'm worried whether I should continue taking it until I see her? I'm not sure whether these hives are a serious warning sign and that I should stop taking them. I don't want to have an anaphylactic reaction :(
You were given beta blockers because they have been helpful to people with social anxiety. It is very possible you're having an allergic reaction and yes, there are other beta blockers. I would consider therapy as well, since that would solve the problem providing it works, which isn't guaranteed but is better if it does than suppressing the problem with drugs that don't directly treat it (and there are no drugs that treat the cause of anxiety unless it's from a physiological problem). I've never taken beta blockers, so I don't know if you have to taper off them or not, as you do with benzos or antidepressants. You can probably learn this by reading the information packet that came with your prescription. The usual way to tell if something is causing an allergic reaction is to stop using it and see if the problem goes away, so you do need to find out if you can just stop a beta blocker or if you need to taper off it. The reason I mention this is, I doubt anyone, your doctor or a pharmacist, can tell you if the drug is causing this -- anything can be causing it. You were already suffering skin problems before taking it. The only way you'll know for certain is to stop taking it and see if that solves the problem, so again, what you need to learn is how to properly stop the drug as an experiment to see if it's the problem. Even if your doctor has never heard of this happening, it could still be happening to you. People differ. Doctors often don't seem to know that.