Yes, I did do that, mine went in my finger nail and out the other side. Like you I pulled back and broke the needle off in my finger. it was very late and everyone was sleeping, I tried to pull it out but could'nt get a hold of it. so wraped it up with the needle still in it and went to bed. Boy did it hurt! next morning said to hubby I broke a needle off in my finger, he went white and off we went to the doctors, I just missed the bone, so was lucky. I now don't sew late at night..LOL
I would say it will hurt for 3 or 4 days and will take time to be able to sew with that finger. doctor will give you some pain pills..
hope yours heals faster and it stops hurting.. Good luck..