The symptoms you are describing could be related to irritation of the nerve that innervates that part of your hand. This is a common problem, and has been associated with extensive work at the keyboard or extensive working with your hands. There are a variety of nerve entrapments that can be found anywhere from the shoulder to the hand and it is best if you are evaluated by your primary care doctor
who will be best able to evaluate your medical history and current presenting symptoms and decide upon the appropriate work up. They may decide that certain lab studies or imaging tests may be appropriate, or they may refer you to a specialist for further work up. There are exercises that can improve and alleviate some of your symptoms, and there are also surgical interventions that are possible depending upon where the entrapment is and the types of symptoms you are having. Other studies that they may recommend include EMGs (which test the ability for your nerves to conduct electrical impulses). Certain medications including NSAIDs also may help decrease some of the burning sensations that you are experiencing so it is important to discuss all these with your primary care doctor.