Had that same injury on my left hand last year. It's an inflammation of the ulnar nerve tunnel.
Now the bad news. The only fix is months of rest. It was around August and I worked as a cargo handler for FedEx, unloading planes, and I had a tough time doing the rest thing. So I played and worked through pain until the season (Canada) ended, and quit my job (for non-injury reasons fyi), gave my hand about 5 months of rest and it's great again.
Rest and ice my friend.
edit: I hurt my hand taking a divot too.