i guess that would be neurologically possible but i can't say this would be a common response to a cold. because of nerve pathways and the tendency for upper respiratory viral infections to cause inflammation in the nose throat sinuses and lungs one might feel responses in the teeth. for instance pain in the molar area can be felt in the ears; pain and pressure in the sinuses can be felt in the upper teeth.
can the common cold make your teeth hurt with all the coughing and blowing done over a week?