My anxiety as a kid wasn't where your sons is (although these days I have, usually mild, GAD), but shots were one thing that freaked me out badly. I don't think I needed to be held down for them, but I know there were tears for ages. Blood draws I did need to be held down for.
What finally helped for me was when I went in for a Hep B series at 14. The nurse who put me so that across from me at eye level was an eye chart or alphabet or some other poster in letters I could read. She had me start reading it aloud. The idea was that while I was concentrating on the reading, she just did the shots. They still hurt, but they hurt less and the distraction kept me from flipping out. Over time I was able to work from reading or repeating something verbally, to doing it internally, to chatting with the nurse or phlebotomist or whomever was coming at me with the needle.
I've never cared so much about seeing it with vaccinations that go into my shoulder, but if it's a blood draw or IV, I do prefer to be able to see the needle. The one time as an adult I really flipped out was when I had a MRI with contrast and couldn't see what they were doing because of how my head was strapped when they put in the contrast IV. The next time I had to have the same sort of MRI, I warned the nurse and she showed me the needle and told me when she was about to inject and it went much better. (MRIs themselves don't bother me at all, it really was not being able to look and know when the IV went in.)
