Maybe start with your family doctor. You may end up being referred to a neurologist if it is likely due to nerve compression. My husband had similar hand pain that went on for years. He is a stubborn cuss and didn't see a doctor until he had trouble even grasping things. He had such bad nerve impingement in his wrists and elbows that he ended up with permanent damage to his hands and permanent nerve pain, even after surgery. His was an extreme case but it shows what ignoring things can do.
Trek Madone 4.7 WSD
Cannondale Quick4
1969 Schwinn Collegiate, original owner
Terry Classic
Richard Feynman: “The first principle is that you must not fool yourself and you are the easiest person to fool.”