This is a long topic for me... All comes with the caveat that I am not a doctor or physio and your problem may be different. No one has said I have arthritis... But as Misha said, my instinctive reaction is caution there - how did they diagnose? Did you have an MRI? You'd have to ask Huffy or James if it's viable to diagnose via ultrasound, it may be. I assume any diagnosis based on symptoms should be treated with a very heavy pinch of salt. I know the hand surgeon I've seen said you need the posh MRI (3T Vs 1.5T I think?) to get a good look in that joint (this was to check I'd not ripped up bits of cartilage or broken a bit of bone off or anything, basically to confirm there was nothing "wrong" with it other than swelling)
I still have chronic swelling in one of my PIP joints, I don't expect it to ever go away, but I can still do a lot on it with suitable choices of routes. For me monos are a no no, small crimps require low volume only, thin pinches require care, and I have to be careful how I train - I've accepted that trying things like Evo or Northern Lights is too risky so I mostly choose things that are steeper and on bigger holds; long steep onsights - fortunately my favourite style - work very well. In the right style I'm probably better than I've ever been, but the range of styles I can operate in has narrowed. Repeatedly pulling on the same holds is where things really get risky. This is also true for training, so I don't really do repeaters or foot on campus any more as the repetition can be very aggravating.
How many injections did you have? I had 2 from Volker (10 days apart), but think I went back to training, especially volume, too fast in the following months. I would advise sacrificing maybe 6 months after injections to gradually building back up if you really want to try it properly. They might help you reset to zero but by all accounts will dehydrate the cartilage and you'll still need to teach the affected cells not to be so sensitised to swelling. Volker was fairly adamant that a single injection very rarely worked well, you need 2-3 10 days apart each, no climbing for 10 days after any injection.
Nowadays I find that if I do almost anything my finger is slightly swollen, say 2-4/10, so it's not feasible to keep it totally unswollen. But then I can do a lot and it stays in that range. Only if I get reckless does it get very swollen... I.e. I can operate anywhere from say 5-85% of my capacity and it stays at maybe 3/10, so I just avoid that last 15% that really sends it over the edge e.g. monos, small crimps (arbitrary numbers but you get the point hopefully!)
Last summer I took 6 weeks off to try a "factory reset" but it came straight back when I started breaking things back in again. Not worrying so much about it and just being strategic with my problem, route and training choices has worked well for the last year. Its comfort zone is definitely expanding, just very slowly.. who knows, if this carries on another few years maybe I can do hard crimp routes again? For me this thing is definitely a long game - it's like standard rehab (find what you can do, do that, gradually do more) but over the course of years not weeks or months. Again for me this means it's not feasible to just rehab on a fingerboard or by avoiding climbing outside as the timescale is too long, it's about making season-long choices about your objectives and seeing where you get to.
Oh, I X tape every session and leave the tape on for 1-2 hrs after the session to help suppress swelling
But of a brain fart there but hopefully something useful or encouraging!