No, I have no problems with seeing blood at all, which is probably good because I have a terrible habit of biting the skin around my fingernails until I bleed. On the contrary, I'm actually kind of fascinated by it and will sometimes squeeze the wound to watch it come out. Of course, that's only with minor cuts and injuries. But I've had more serious injuries, like once when I cut my hand open on a glass bottle and I bled for a very long time and the blood didn't bother me at all. I was just concerned about how much blood I was losing.
I do not like getting my blood drawn, but that's more of an issue with needles. I can't watch needles going into the skin so I have to look away when they do that part. Once the needle is completely in, I'm totally fine, though.
I used to have this very badly due to some very unfortunate circumstances of my past. I would shake, get sick, and sometimes (rarely) faint. After some reconditioning, I’ve overcome my fear of blood and only think of it in terms of cells and their components. I find blood cells and their abilities very interesting now!
I am a bit unsure if I have a blood phobia. When I was a kid, I went with my best friends (they were sisters) to their doctor visit and apparently one of them was getting a butterfly shot. I had no idea what that was but I watched intently as they drew some of her blood. Then I stepped out in to the hall, my vision went black, I was super dizzy, and I fell over and started throwing up and you know what, the doctors just stood there looking at me like "wtf" instead of helping me
So ever since then I just don't look when someone is getting their blood drawn. But I can watch gory scenes in tv shows and movies for the most part
For some reason my own blood doesn't bother me that much but seeing it come out of someone else makes me uncomfortable. I don't think it's anywhere near a phobia though.
Oddly enough, as a child, the sight of any blood made me squirm and gave me chills. As I've aged, it seems to have diminished more and more overtime and it doesn't even bother me anymore.