I hate needles too, but I've had to experience them several times over the last year, with wisdom teeth removals, and also a few blood tests as well. I've learned to deal with it now, though. I literally just look away and sqeeze something tight in my free hand whilst reciting something in my mind, and it's bearable.
Try having the blood test. It's not that bad as you think. You could ask your doctors if you have carpal tunnel syndrome. This is where tendons in the hand are too tight so they can get 'trapped' in the hand, causing pain and restricted movement until they go back to normal, or, they are too tight to cope with activities such as a lot of writing/typing or carrying things, and they are made sore. This is a bit like RSI, but is the tendons not being able to cope with something that they should be able to.