Is having a toothache a symptom of mouth being small?

No. Generally toothaches are due to tooth decay, it is unusual for mouth size. It could be due to tooth crowding and to be honest the best person to ask is your dentist - medical school provides very little dental training.
Not really. Having a small mouth does not cause a toothache. Having an incorrect bite because your mouth is too small for your teeth can cause a toothache. I would recommend seeing a dentist for an evaluation because likely the tooth ache, no matter the cause, won't go away.