Disclaimer: ***I'm not a medical expert***
From what you describe, I have this exact same problem and you need to get it seen to straight away.
It's not carpal tunnel, it's ulnar nerve compression. The carpal nerve often gets compressed at the wrist joint, and results in numbness/pain/etc. of the whole hand EXCEPT the pinky and one side of the ring finger.
The ulnar nerve is commonly known as the 'funny bone' and is most commonly compressed at the elbow. It results in numbness/pain/etc. of the pinky and the side of the ring finger closest to the pinky.
While this compression can also happen at the wrist and the shoulder/neck, it is most common at the elbow and your symptoms seem to support this. If it's not fixed you will start to notice clumsiness in your ring and pinky and eventually, in really bad cases, the muscles on the back of the hand will atrophy and your ring and pinky will curl in towards your palm and not be able to be used.
Most of the time the problem can be fixed by changing your posture, but sometimes they will do a surgical procedure to move the ulnar nerve to the inside of your elbow.
In my case, I noticed tingling/pain in my left ring finger first then the pinky. Then it got a lot more specific, and I became numb on one side of the ring finger and the whole pinky, extending down my palm on that side, almost as if there was a line down the middle of my ring finger to my wrist. I also started to notice that even though I was doing exercises to improve finger dexterity and speed on the bass, I seemed to be getting worse instead of better.
I went to my doctor and he referred me to a neurologist, who did a series of nerve tests. They basically put electrodes on your arm and then give you mild electric shocks at different places. They then measure your response and compare your arms to a normal response. Sometimes they will insert a needle electrode deeper into your muscle to get readings (this is uncomfortable but not agonising). The weirdest thing is watching your arms jump all over the place as they zap you with a mini cattle prod!!
In my case, I had no sensory responses coming back from my left hand above the elbow, and I had diminished motor responses getting to my hand from above the elbow. They showed me the graph of the nerve responses - I could quite clearly see the tops of the waves were being chopped off and the wave was actually delayed compared to my right arm, which pretty graphically explained my fretting hand clumsiness.
After that, the neurologist watched how I worked at a computer (I'm an IT nerd in my other life), and found I spent most of my day with my left arm bent tight and often I would support my head with my left arm and almost grind the elbow into the desktop!! That stopped straight away!! He also found that I slept with my arms bent and my hands almost under my chin - I blamed this defensive posture on my wife thrashing round beside me, beating me up
I ended up needing to wear a soft splint (actually it was one of those neoprene sports braces for your knee) on my elbow to keep it straight as I slept.
Good news is that it took about a year but I am almost good as new. I still have a little 'tenderness' on the tip of my ring finger, and sometimes I will wake feeling numb but then I put the splint back on for a couple of weeks to retrain my arm to stay straight.
Better news is that he told me that the bass practice was actually helping me and to keep it up - the playing was keeping the muscles on the back of my hand in condition.
Best news was that when the nerves started to repair, the clumsiness went away and all that practice I had been doing showed itself
So get it seen to man!!!!