Having a piece of fiberglass in your finger would definitely cause local inflammation that could take some time to resolve after you've pulled the piece out, depending on the size of the piece that was embedded and how dirty it was. It is certainly possible that you have a small fragment that is still in there, which would manifest by continued pain, redness and swelling. It is also possible that the piece that embedded itself into your finger was dirty and that you either have some dirt or debris stuck in the wound or that you are developing an actual wound infection. Signs of an infection would also be redness, swelling and tenderness to touch, and signs of a serious infection would be if the redness and swelling start to travel up your finger. A very bad sign would be if you start to get fevers or shaking chills, or if your finger or hand starts to hurt even to light touch; you should go right away to the emergency room if you develop any of those symptoms. If you don't have fevers or chills but continued pain, it's worth going to the doctor
and having them examine your finger; it can be difficult to tell whether there are residual pieces left, depending on the material, but sometimes the pieces can show up on x-ray
and it is important to make sure that nothing else is lodged in there.