Will This Eventually Work Its Way Out If It Is Present? Does A More Active Intervention Need To Occur Surgery?

Question : I impaled my right index finger between the first and second joint, palm side, with a large splinter from construction lumber. It went very deep and the finger bled copiously when I pull the large long splinter out. Three days later, the whole finger was angry, red, hot and swollen. Ten days of antibiotics calmed it down but 4 weeks later, it is still sore, swollen and warm. I assume there is a remnant of the splinter remains. My question is how would you recommend I proceed? I know that wood doesn’t image with xray. Will this eventually work its way out if it is present? Does a more active intervention need to occur (surgery)? Perhaps the splinter doesn’t exist and this some type of ongoing reaction? Any comments about possible progression and/or actions needed would be welcome.