Why do I almost faint when having a blood test and would I have the same reaction to giving blood.

Almost without fail, if I have a blood test and I'm sitting in the chair, at some point I'll start to feel very faint and weak, my blood feels like it is rushing around, my vision will blur and I'll come close to fainting. I've never actually fainted but I have lost control to the extent that falling out of the chair was a very real possibility.

I can't figure out if it is psychological (looking at the blood vials seems to make it worse or bring it on, on some level I do start getting paranoid that they are stealing my blood, even though intellectually I know this is ridiculous) or physiological. If I lie down on a bed while giving blood, it feels much better but I still get faint. Every time I give blood now I tell the nurses that I need to lie down in advance and they seem to indicate that this is rare but not unheard of.

What is the mechanism behind this? My blood pressure was normal last time it was checked so it is unlikely to be that. I would love to donate blood at some point, but I feel like I might actually pass out if I do so.