wine glasses black stem

I was recently polishing a wine glass at work and the stem snapped. It took me a second to realise but a long piece of glass was sticking out of my hand in the pad bit under my thumb where my wrist goes on to my hand. It must have been so sharp because I didn't feel it go in. I went to the sink and pulled the glass out and blood that was so dark it was almost black started pulsing out of my hand - I washed it quickly and then put tissue over it and held it firmly for a bit and then put a plaster on. I think I may have cut the vein in my hand, my hand is really weak now (about 3 days later) and is really bruised around the vein and it's swollen. Have I damaged the vein irreparably?