I had the same problem. I still have a visable scar on my hand and it has been two years since I remedied the situation. The problem had nothing to do with a drop of glue, how many feathers, or which wing of the turkey was used. No matter what, I was going to be bleeding.
I finally figured out that I was putting too much pressure on the bow string with my index finger, which was causing the arrow to come off the shelf in a manner that would allow the arrow to violently get into my hand. When I really started concentrating on putting nearly all of the tensinon on the string with my middle finger the problem was solved immediately.
I seemed to develope this problem over night and lived with it for several months. I KNOW without a doubt this is what was causing my problem, because I can make the fletching cut my hand any time simply by putting about half the tension of the bow string on my top finger.