Could also try shooting cock feather IN. That might be a quick fix, at least.
Your painful problem is one of my fond memories of starting archery as an 11 year old boy. Had a $10 "Cherokee" wood bow from a souvenir shop with 3 wood arrows. Every time I shot, the quill would cut a new furrow into my skin, usually bringing blood, but always pain! Didn't matter, didn't matter! I shot over and over just to watch the arrow fly.
Good news is, you shouldn't have to go through that to enjoy archery with the advice you've received here. Enjoy the new bow!
Daryl