I have to have blood tests all the time, and at first im always a bit scared, but you just have to remember it doesnt hurt that much. It hurts less than cutting yourself, or having a really bad headache.
Its true that you don't feel them changing the tubes, or taking it out, its just like a tiny scratch when they put it in. Just look away, and try and talk to the nurse or whoever you are with.
You're 14, so its likely that you will be treated as a child, in which case they migt offer you 'magic cream'. This numbs your arm so you don't feel the prick of the needle, but imo it feels worse having a numb arm than a scratch!