Hi Colin,
I'm needle-phobic too, so I completely understand. I used to faint whenever I had blood tests - then someone told me I could have them in the back of my hand instead of the crook of my elbow. I tried it - and I don't faint any more. I don't even need to lie down any more (I just don't look). I've no idea why this is - it actually is more likely to hurt in the back of the hand, but it just doesn't have that awful cringy wanting to curl up and howl and then vomit and then howl some more feeling that a needle in the inside of the elbow has for me. Might be worth a try?
I also find it helps to do breathing exercises while I'm there - take a deep breath, thinking "I relax my ... ", hold it for a second and then breathe out, thinking " ... head" (then gradually work your way down!). And tell them in no uncertain terms not to say "sharp scratch" just as they stick the needle in, that always makes me tense up. Much better if they don't warn you! Better still if they are chatty and can ask you a question about something completely unrelated just before they start.
I thought I would never be able to cope with being diabetic, but I am now giving myself 4 injections a day, thanks to covered needles which means I don't have to see them going in. If I can do it, believe me, anyone can!