Take the time you need to recover. You can do some work on your game if it doesn't requires the use of your injured arm: for example doing some voice recording either for in-game use or to record your ideas in an audio file.
I hope you get better.
If you’re the type that’s gotta keep themselves busy, this is a pretty good way to think about it. I had a lot of hand/wrist issues for a few years (still do, but fewer and less severe) and finding new ways to work on my stuff while minimizing the impact on my health was a huge help.
One specific thing you can do if you’re working on a narrative-heavy game is use dictation to transcribe your earliest, roughest drafts. The average dictation tool won’t get every word you say right, but the errors are pretty easy to fix and it’s not like your first pass on a piece of text is likely to be what goes in the game anyway!
With that said, I will note that OP’s case sounds pretty temporary so it might be easiest just to think of this as an unexpected opportunity to rest.