You definitely need to get in to see your primary care doctor
about this problem as soon as possible. There are several potential things that could be going on, but the fact that you have burning and numbness
in the hands suggest that this may be a nerve problem.
Based specifically on where the pain and discomfort is in your case, I would guess that the mostly likely possibility is something called carpal tunnel syndrome
. Carpal tunnel syndrome is a condition in which the median nerve, which is one of the large nerves running down the arm into the hand becomes pinched or compressed. When this happens, there is typically pain or numbness in the palm of the hands and also in the fingers that you mention. Carpal tunnel syndrome often may be most noticeable at night but, as it worsens, the symptoms can occur during the day as well. Carpal tunnel syndrome typically occurs due to an overuse injury at the wrist, often from repetitive motions like may occur with typing at a computer or with fine sewing.
Your doctor will be able to examine you for signs of carpal tunnel syndrome, as well as other potential problems, and suggest next steps for work up and treatment.