For a case like like that I would definitely see a hand surgeon.
I saw one back in 1997 when I had a paraesthesia (a kind of numbness) of my fourth and fifth fingers. You may be interested to know that those fingers are supplied by the ulnar nerve and the other three by the radial nerve.
There were a lot of investigations to try to determine where the impingement was (it can come from the neck, the shoulder, the elbow or it can be local). Some of those tests were quite nasty.
But I have seen them do a carpal tunnel release in theatre. In some cases that might be of benefit. I would check it out.