Hello, Welcome to Just Answer and thanks for your question. What has your medical provider given you as a diagnosis for the burning? What is your age? Do you have diabetes? What tests have been done so far?
Thanks for the additional information. Without diabetes neuropathy, or another nerve neuropathy, or Raynaud's phenomenon which also causes a feeling of cold hands and perhaps a bluish color, then anxiety is likely to be the cause. Simple things like immersing them in cool water may be all that you need to do. If there is pain, most people can tolerate acetaminophen (Tylenol). If it continues, a referral to a neurologist for nerve testing may be in order.
Yes, stress/anxiety really can cause physical symptoms. Diabetic neuropathy (which you can't have since you don't have diabetes) occurs when high blood glucose over a span of years damages nerves resulting in pain/burning. Raynaud's phenomenon is a spasm of the muscles in the walls of the tiniest blood vessels causing blood to be backed up in the part of the body affected so it cannot get back in the circulation. The hands generally turn bluish color (especially the fingers) and can hurt.
Some other neuropathies (nerve pain) can be from nerves damaged from any number of different things. A nerve test at a neurologist's office would determine if this is from nerve damage or not. There are prescription medications like gabapentin that can help if it is. There is nothing available over the counter that would help.