Does your ear have to be a certain size to get your tragus pierced?

It's called a Tragus. The lip of the ear canal should be predominant and should move freely to cover the canal when pushed by the index finger. If the tragus is too small then healing and rejection could be problems. Only a professional body piercer can make that call by looking at your tragus. Do not pierce this with a piercing gun, there are a great deal of nerves and vessels in this area of the ear and a piercing stud can and will do serious damage that can not be repaired. Piercing guns are for ear lobes only.