I never ordered my daughter's real birth certificate?

You don't say how old your daughter is. The hospital filed the birth certificate with the appropriate authority in your state within a few days of the birth. The first thing to do would be to order an official copy of that certificate. The Centers for Disease Control has an on-line list of where to write, listed in sources. Once you find out what the current version of the certificate says, you can have errors corrected. Exactly how to do that varies from state to state, but often it is fairly easy to fix errors during the first year, and after that you often have to go to court to make changes.