A few weeks ago, I had an accident at work that left deep, long gashes down the inside of my index finger and inside of my pinky knuckle. The stitches came out ten days ago, but I'm still struggling to regain my playing form. The index finger can't handle barring strings, or any similar motions, mostly due to arthritis-like pain in the DIP joint (nearest to tip), and my pinky doesn't have sensation in the palm-side of the finger pad due to severed nerves.

This is effectively leaving me with two functioning fingers, with some occasional spot-work from my index. I'm beginning to become discouraged, and I'm holding my guitar for shorter and shorter periods of time before putting it down in frustration. I know I'm not the first guitarist to have to rehab their playing hand, and my injury is certainty not the worst that someone's had to overcome, but I'd really appreciate some tips, advice, or stories you folks may have to offer up, particularly related to playing/rehabbing a numb finger or dealing with arthritis-like pain. Thanks in advance, folks.
First of all, don't give up: see Django Reinhardt, Tony Iommi and Dave Mustaine.

Second: make sure you get enough rest.

Third: get a grip strengthening device of more kind that lets you work individual fingers.

Fourth: you might want to talk to a health-care professional.

In the event that you have permanent lingering effects, you might have to adjust your playing style- see the first point I mentioned.
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I broke a few bones in my fret hand last summer, takes a few months to get back to full pace. And I had clean breaks, you migh have some muscle damage so will need to start building up the strength and control over those muscles so maybe visiting a physiotherapist or an occupational therapist might be a good idea.....It's tough dude, I was playing with a really good band at the time so I was afraid I would get canned. Keep with it lad and I hope it heals well for you.

Note - I find I dont use my ring finger as much since, I dont know if its range reduced from the break or did I just get used to using my pinky so much it has just become natural, your body finds a way to adapt maybe.
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You're certainly not the first to have come back from this, and you won't be the last.

In a couple of aspects, it's going to be like relearning the guitar, so you're going to have to go back to basic exercises, watch your hands until the muscle memory and your hearing take over from what you used to be able to do by feel. With the pinky, it's going to be a bit like the first time you forced yourself to practice without looking down at the fretboard. It'll find its way. With the barre chords on the first finger, it's going to be a case of pushing through as much as you can until it heals and the pain goes away. Arthritis-type pain can be difficult, but a lot of folks rely on soaking in hot water (and there are warm paraffin bath devices specifically for this) prior to practice or playing.

Determination conquers debilitation. Keep doing the work to get where you want to be.
Use whiskey and drugs to numb the pain and just play......

But really TS, just keep using those fingers in everything you do. The hand strength tool is great advice. You can also put a large rubberband around all your fingers and do individual movements.
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yea use the fingers more and eventually they will get stronger. even with out injury just putting fingers in a cast or splint for a time will make them tender. I had my index finger cut off on my fret hand that was sewn back on... as long as I use it alot it stays strong if I start babying it it gets sensitive. Don't give up it is going to take months to make that new skin like you need it.