It sounds like you may have a fleshy tip on your upper lip. This is an hereditary trait. You might have been told to play clarinet in grade school because of the tip.

You can get around it by playing to one side. Roger Voisin played to one side and so did Maynard.

This link shows Cupid's bow on a female. It is not as bad as can be found on men.'s_bow
A Cupid's bow is a mass of flesh attached to the vibrating lip of the player. The mass inhibits the vibration of the lip.