I was pretty phobic about needles when I started injecting, but I found a couple of things helped a lot. Before I started, I spent some time watching YouTube videos of people self-injecting, as a way of desensitizing myself to the sight of the needle going in and getting familiar with the process.
I do mindfulness meditation pretty regularly, and that helped a lot, especially at first: just sitting with the fear, feeling it my body and breathing into it, then visualizing myself doing the injection, and getting comfortable with the feelings from that. It also helped me to focus on relaxing the thigh muscle before injecting -- if I'm relaxed and warm, it mostly doesn't hurt.
Lately, I've been working on getting over the hesitation thing: where you start to inject, freeze, try again, freeze, etc. I've been visualizing putting the needle in very smoothly, and then actually miming the gesture, without the syringe. Then I go to do the injection, and if I hesitate, I start over with the visualization and miming. This has helped me a lot. After 3-4 weeks, I can now just pick up the syringe and do the shot without freezing or flinching.