How can I find my 1/2 sister who was adopted at birth with only my mothers maiden name?

and my sister's approximate year of birth? My mom received 2 phone calls recently from a girl who was crying hysterically on the phone, and she said "hi grandma, this is your oldest granddaughter". My mother has no idea who it was, as mom just has 1 granddaughter, which is my daughter. I am concerned, because of it possibly being the daughter of my 1/2 sister. This girl called back twice. I am thinking that my sister may be trying to locate my mom, because of medical reasons. I don't want mom to know that I am doing this. But, if this girl needs help, I want to help her. I am unemployed at the moment, so, my resources are limited. Can anyone help me? Any suggestions would be greatly appreciated.