Typically these procedures are done in emergencies and fast paced treatment, due to not being able to find a vein. So there wouldn't be time for a local anesthesia in a real case scenario. Although if not a complete rush and emergency, a local anesthetic can be requested and administered.
My gosh, you are so cute! and brave!!! I would love to learn more about what happened. Did you have the surgery? Are you ok now? did they do it on your birthday? You should be a spokesperson for tubes! (and how old are you?)