Skin Around Claw is Raw, Swollen, and Red

Hi everyone, I am new to this site and saw that ya'll seem very knowledgable about cat injuries. I recently noticed that one of my cat's claws is very red, swollen, and tender on the edges. It isn't the claw itself that looks bad, but the furry part around it that is very, very inflamed. I think that he has licked it raw and it is now seeping blood droplets. He does not seem to be limping or having any trouble walking, but he does use the scenic, least impactful route when jumping from thing to thing.

The only parts of the claw that are visible is a very short and thin piece, so I'm thinking he might have ripped his claw out on a tree or something. I have had a cat do this in the past, but the skin around the claw did not behave this way.

Any help or ideas as to what this is is much appreciated

That's nasty.  If he were mine, we would definitely be going to the vet tomorrow, and I don't go to the vet that often, I treat most things at home.  How it happened is not nearly so important as what to do about it is.  It does need treatment.