My reaction to my own blood is the same as my reaction to anyone else's blood: "Someone's injured, I'd better get out the first aid kit." If it's a small cut (such as the one I got shaving the other day), it's more of an "eh, it'll heal," whereas big, gaping wounds put me into crisis mode -- by which I mean I mentally and physically enter a state wherein I am ready and able to do whatever is needed to end the crisis (in this case, it usually involves bandages and/or steristrips), not that I lock up because it's a crisis.
That response is so pronounced in me that I seriously considered a career as an EMT at one point.