Hi and thanks for the question,
I think the flight will really have no impact on your health condition and you can actually fly. If the pain increases so much in intensity, it could be advisable to add an analgesic
to your treatment. If pain increases or persists, finger continues increasing in size or you notice some pus, it shall be worth consulting your family physician for appropriate antibiotherapy and other measures if necessary.
You can fly without any fear or worries.
Thanks and best regards,