K.R.
Hi A.-
I worked for a pediatric dentist for 5 years, and we never used nitrous oxide. There are different studies being conducted about the negative results of nitrous oxide. Usually a dentist will use topical which is a cream to numb the area before giving a novacaine injection, so you don't feel the injection. Maybe you should have your daughter see a pediatric dentist who are used to working with small children, (usually starting a 3 years old) instead of a dentist who usually sees adults and have a different tolerance for "pain".
Hope this helps
K.