Busted both mine at the same time after a climbing accident. Having two hands in plaster is a real pain in the arse.
Left one healed in the cast and was in for roughly 6 weeks, right one needed quite a lot of surgery and thus was in a few weeks longer.
Both have healed fine, I’m stronger now in both, although with a little less flexibility in the right.
Used gentle climbing as a way to increase strength and the consultants were amazed at the speed of the results.
So take it easy for a while, but do the physio and train it went told to.