vital statistics question

I was given up for adoption pretty much right after i was born, i never went home with my mom or anything, i went straight to foster care and was adopted 8 days after i was born. however, i know i didnt get my birth certificate to reflect my adopted name until i believe almost a year after i was born--at least i know it was a good amount of time. my question is this, in the vital records (i am looking on rootsweb) i am listed with my adopted name, but is another one of those names on there me before my name was changed? i want to know because i know my moms first name and i think i know the year she was born in, so i could go through and compare and see how many people with her first name have a last name match with someone born on my birthday, you know? anyway, if anyone knows this, this would be very helpful (oh also, is there anyway to search using my birth number? i went to my library to use the microfiche machines but they said they didnt keep birth records there, even though i had thought someone had said they did. the lady there suggested the nearby mormon genealogy place, any ideas? thanks a lot guys...) rachel