Are you using one needle to draw up and a fresh needle to inject? I would use a fresh needle and the smallest gauge that's practical to inject. That means less pain.
I was getting tense about something else and my psych suggested guided visualization. You can find this on Youtube, for example a guided visualization of being on the beach. The beach isn't my happy place so I tell myself I'm in an overcast, brackish marsh (hey, it's my personal calm place). Tricking yourself into calming down will help with muscle tension and pain later.