Thanks for your question. This is certainly an interesting question, but not one that is unheard of. There are many potential explanations and I recommend speaking with your doctor
to determine the best course of action. The sensation of pain and discomfort is carried by nerves to the brain, which allows the body the chance to alter and adapt to the stimulus in order to protect itself. When this is extrapolated down to the larynx (the part of your throat that is involved in making speech and sound specifically is known as the glottis, with the larynx the broader region of the throat that is closely associated), it is apparent that there are really only a couple of nerves that are involved in sensation. The pain can therefore be readily localized to a specific nerve branch, which can give some clues about the area of the pain. At this point, a physical exam by an ear nose and throat surgeon
(AKA ENT AKA otolaryngology head and neck surgeon), specifically a laryngologist, would be necessary to determine if there is anything specifically wrong in that part of your body. He or she may feel that some sort of radiographic imaging would be helpful. Please speak with your doctor to determine your next steps.