I had a school friend who used to hit the deck at the sight of a needle, he went on to be a phlebotomist and is now training to be the world's oldest newly qualified nurse. I don't mean to be a dick by mentioning this, just giving a story of someone who overcame this phobia. I don't know how he managed it, but I would guess that gradual familiarisation would be it. I can ask him if you're interested in the answer.
I had my first jab today (go team Pfizer...wooo!), the place you had yours sounds very well organised. When I arrived for mine, I walked past someone sat on a step looking shakey with a glass of water! The holding cell for the 15 minute cool off was dodgy too - no ventilation and the only free chair when I arrived meant that I sat well within a metre of the door and had the pleasure of subsequent injectees walking past me. I felt no compunction about being "that person" who opened the exit door with his elbow and closed it with his boot.
Until opening this thread this evening, I didn't know that a nocebo effect was a thing, but can see how it can be. Within less than a couple hours I noticed my shoulder feeling dodgy when I tried to put my hands behind my head, and then some weird sensations in that arm which have cleared up now. Fingers crossed a trick shoulder is all I cop, I hope you're bearing up by now. It's making me feel quite nostalgic for my rugby days, when I would wake up the next day feeling fine, then move a body part and realise I had a pain in it!