Hey, I'm pretty old for this game, so my hands probably take longer to recover than others. I've had to see a physical therapist in the past for issues I gave myself from osu + typing for work. I would definitely recommend that for you. Any pain that lasts longer than two weeks is worth seeing a doctor about, especially if you feel it even when you aren't playing. They will be able to give you good advice and exercises and get your hands stronger. Don't be scared about going, you aren't going to have to quit the game and a good doctor won't be judgmental, just follow their advices. It is not too late, you can recover from this problem.
In addition to the exercises they gave me, something that has helped me avoid injuries for a year now is to start out really slow. I usually start my session with two star maps and gradually work up to three and four star for about an hour, but what really slow is might be different for you. I find it helps me to get into the session with comfortable tapping and aim as I can begin to fix all of the small problems in technique before I even start playing "for real". I have tried warming up like others do and jumping right into the game, but it has always led to injury, I need to do a "pre-warmup" personally.
+ If the doctor says it's okay, I would really recommend using a gyro ball for a few minutes a day. If not okay, start using one when your hands are all better. It's been a lifesaver for me. Look into "neuroplastic pain" as well. Sometimes even if injuries start as real injuries, your brain can become "trained" into having chronic pain or trained into the pain feeling even worse, because you are so afraid of it. It might not be the case for you but it is worth looking into in addition to seeing the doctor.