I had similar symptoms to what you describe and it was not CT, but a different kind of nerve damage. Proper diagnosis is critical- it is worth the time/ hassle/ $ to see a proper hand specialist.
They did an EMG on my arm to see what nerves were being compressed. (I can’t spell, but I think it is electromyelogram)
Then I had a brace 24/7 for 6 weeks.
Then, about 3 months of intensive PT. ( 2 or 3 times a week)
The treatments included traditional exercises and conditioning, as well as acupuncture and massage. While I was skeptical about the acupuncture- it REALLY did help with the pain.
I still have occasional pain/ numbness and sometimes wear the brace if I’ve been overusing the hand. but it is so much better now.
Definitely try to see a specialist- a neurologist or a hand surgeon.