Hi I know totally how you fell.
With Covid taking over parts of Aus I've been staying in my suburb and haven't been in any situations with lots of people. So the whole idea of masses of people is definitely not a nice thought, I can agree with you there. I struggle with similar anxiety, being stressed around people a lot and I find myself worrying to quite a large extent, specifically about things that could go wrong. Try to think about how well it will go and how you will feel after.
It's great to be doing the breathing techniques and it sounds like you have that mastered, I've had lots of different advice given to me, and sometimes just changing your thinking can help. Accepting that this is a big task, but once you have been vaccinated how much safer you will feel. It is great to be doing something like this, and will inevitably help our lives return to some sort of normal.
I've had a few people tell me that overstressing and having high amounts of anxiety over something in the future will only make you put yourself through the experience more than once. Possibly ignoring the situation, until the morning of and then imagining a smooth run through of how you vaccination will go. More practical things to put in place, double masking can help some people feel safer, socially distancing, and not feeling worried about telling anyone there that you are stressed about the situation.
Taking time before friday to relax and make your life as calm as possible, keeping conscious thinking and (i know it's cliche) but only thinking of the positive aspects of being able to get vaccinated.
I hope something I've said can help in some way.
You have got this, you are brave, and I'm sending virtual hugs and support your way.
Best of luck, via :)