Hi Milo! A fear of needles is more common than you think! One thing you might try, is to bring some music with earphones and listen to music while it's being done. Spend some time talking with the person who will be taking your blood, let them know that you're fearful. Try reading before you get called to go in, just something to relax your mind.
I find it helpful to concentrate on the other side of my body ... Even going so far as to relax the side they are taking blood from, but tense up the other side (not easy to do,so it takes concentration)
Try the cough technique. A single warm-up cough of moderate force followed by a second cough coincided with the needle puncture. There's been good reports that this has been effective with reducing the pain.... And they are not sure why it works.
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