Sorry to hear this Ockham :( 

If you feel the need to rest the left arm the pain must be significant.

I wouldn't dismiss it for too long.  Someone I know thought his injuries would just get better in time   and ended up having to have an operation  on his shoulder a few months later.  Not meant to scaremonger, just that insurance could present difficulties if you don't  have it checked out in a timely manner.

Like  questioning if  your injury really occurred at the time of that accident etc.  They can think up all sorts of reasons  to block claims.

Just confirmation that everything is ok is also reassuring.

Hope it's all better soon. :)