while preparing fish, a bit of a fin got in my finger I couldn't remove it all. Will it work its way out or should I see a doctor?  

See a doctor. You should see a doctor. Retained foreign bodies can get to be a nuisance for you if not removed completely. I have had many patients who came to me complaining of this sensation of always having something stuck in there. Often we have to get x-rays and explore under local anesthesia. They can cause local inflammation or infection. Tetanus is a risk too if your last tetanus shot >10 years.