Hello, I am pretty sure your epiglottis has nothing to do with stuttering. There is a very high variability of epiglottis shapes in people. The function of the epiglottis is to block the airway to protect stuff in your mouth going into you trachea and then lungs. The pressure you feel when trying to speak make either be muscle tension in your diaphragm or your vocal folds not allowing air to pass through.