While I am primarily right handed I do use my left hand for a number of things (This is mainly because I use a reasonable amount of tech and keep relying on one hand can cause pain, which is why I tend to split the tasks between both hands.

Hopefully it is not as bad as it seems and you get over it soon, just don't go faster than recommended (Use it before its suitably healed) as it may make things worse.

Using your left hand to play while the right hand heals should definitely get some positive comments.

Bill