hmmm, interesting. So no pus, can't be a real bad infection. No discoloration so probably no sepsis. Obviously some sort of inflammatory response. As other writer suggested, lymph massage, it looks like lack of lymphatic flow ?
Possible there is some corpuscular encapsulation on a micro level. One option to consider maybe trying might be.... to put it in an ultrasound bath. The type you see at the jewelry store or dentist office. If there is some encapsulation and if its thin enough, the ultrasound might break it up and restore normal flow. Two minutes should be plenty, fingertip needs to be submerged in the water.
Next option is exercise it. Place four fingers of that hand on the top of an opened door. and pretend to pull onesself off the floor using only those four fingers of that one hand. Probably can't lift onesself off the floor that way, but nevertheless exert the same type of force on the top of the door with those fingers as one would if one were able. Repeat. Then, remove the pinkie and only use three fingers. Repeat. Then, remove ring finger and pretend to lift onesself with index and middle finger. Repeat. Then finally, the one finger only. Do it towards the hinge of the door so the hinges don't get bent. Alternately use the top of a cabinet.
Third option is put a pot of water on the stove and turn up the heat high. Immerse finger, keep it in the water until the temperature rises, rises, rises until finally can not stand to keep it in there any longer.
Fourth option, same as third option but when the finger is removed from the hot water, have a glass of ice water nearby and plunge the finger quickly from the hot water into the ice water.
Fifth option is opposite of fourth option. Start in ice water, then go to the hot water.
good luck, I am not an MD, this is only what I might try personally if it were me.