You bring up a good point. I ultimately oversimplified my post to illustrate the point which upon reflection was probably not the best idea
Your presentation is not uncommon at all. It is totally a thing to fear the needle and not fear the pain. Ultimately the strategies remain the same (which is why I kind of glossed over this but it was still a bad idea to do so, my bad)
In addition to desensitization you can also try diversion in the short term. Create sensations in other areas of your body to divert your focus away from the needle. Put an ice pack on your thigh or something similar that’s not harmful but mildly uncomfortable to pull focus. Similarly you can just go with good old distractions if possible like watching a video while looking away. This isn’t the best strategy, especially long term because in some cases it can worsen the stimulus you’re anxious about, but in a pinch it can be helpful. And of course if your phobia is trauma related processing said trauma is helpful (although that in and of itself is often a desensitization process fyi)
According to another comment reply that info is out of date