With a razor blade, bevel the angle of the quill of the feather that is causing the problem (and the other two if you want to) so it smoothly mates with the shaft, with nothing sticking out to snag your finger. Then put a drop of glue on it and let it dry. Then burnish the glue down with the back of a teaspoon or something until it is flat.
If that doesn’t work, wear a thin glove, like a golf glove, on your bow hand.
You should be using a 5/8” nocking point and nocking under the nock point until you figure out something you like better.