I used to hate injections of any sort - ever since a child - and go to great lengths to avoid having them, and kicked and screamed and cried as a teenager during my heaf test! I trained to be a nurse, and not only did I have to have about 6 before I could even start, I had to learn how to give them to others - the phobia quickly went because I had no choice but to deal with it.
There was a similar attitude towards it on the TV show 'Shameless', with an agoraphobic woman who wouldn't leave the house. Her children pretended there'd been a terrible accident outside and she *had* to force herself to go outside - after much huffing and puffing, she went, and was fine.
It's a type of behavioural psychotherapy, which claims that the symptoms of a phobia (sweating, dizziness, crying, or whatever) can only last for so long before your body returns to normal. It's cruel, and a bit of a short, sharp shock, but it really does work - there were many case studies of medics pushing water-phobic people into a swimming pool. After they screamed and flapped around for a few minutes, they soon began to calm down and eventually were fine, having overcome their fear. Not sure how you could do it with blood though, unless you buy something raw and bloody from the butchers - you either get over your phobia and clean it, or you go hungry!