Thank you for your reply to my question. Since I originally posted my question, I have obtained my grandmother's exact birth date, found the county in which they lived (and presumably where she was adopted). I contacted the Division of Vital Records and the lovely people there helped as much as they could. Long story short, they searched for adoption records, birth certificates with girls having her first name on the specific birth date, and found nothing. There were multiple girls found born in the state on her birth date, but they could not give me that information. We ultimately decided there was no formal adoption, as happened at that time.
I was lucky enough to find her listed in a school census posted online, contacted the school superintendent's office, and was given copies of her school records (under her adopted surname) for the years she was there.
Everyone was very helpful. I would encourage anyone in a similar situation to contact the Division of VItal Records. They were very interested in helping find the answers to my questions.
Suzanne