I was knocked by the door a month ago, but my middle finger is still swollen and painful. should i see a specialist or gp?

Consult a hand specialist for evaluation & proper treatment. The goal is to avoid chronic irreparable damage to your finger which can lead to lifelong pain & limitation of function which lessen hand strength.

Start with GP for an exam and possible tests, such an X-Ray. Based on findings and goals, your GP may recommend a local hand surgeon.