I've never had a serious injury to either hand, but I do have chronic pain in both index fingers and my left thumb and mild carpal tunnel syndrome.

I'm not a big believer in "exercises". I believe the best "exercise" is to do the thing itself, whether it's drawing, playing music or whatever. I do recommend scales and arpeggios, and practice them myself, but I don't consider them exercises.

Apart from that, something an orthopaedist recommended and I still do sometimes is to squeeze a soft football (a real football, not a soccer ball) filled with soft styrofoam, or something like that. The pointed ends are handy. It's a rather dull and stupid exercise, but it seems to help.

Otherwise, I have had very good results with qi gong balls. I prefer the heavy stone ones to the metal ones that jingle. The bigger the better, but it may be smart to start with small ones. Helped better than anything else with the pain (except for pain-killers).

After a moth infestation, I did eventually discover that they were coming from the wooden box one set came in.   I have not had any problem with any of my others, though.

I also occasionally use a device for weight-lifters, boxers, etc., for strengthening the hands. It's a spring with two handles that you squeeze. They come in different "strengths". The really stiff springs are nearly impossible to overcome. One should exercise care with these devices; they can be great, but one can hurt oneself by trying to do too much.

As with any exercise like this, it's much better to do fewer repetitions slowly. It's not much use to open and close them quickly.

If you've always had trouble with a full barre, perhaps your guitar isn't suitable or set up properly for you. A thinner neck, and/or one with a "camber" (i.e, a concave surface), and/or lower tension strings might help. You might have to accept a little bit of fret buzz, but it might be worth it. A good guitar-maker, repair-person or even a knowledgeable salesperson at a guitar store might be able to help.

I wish you a fast and full recovery.