Birth Books in Austin

I am planning a trip to Austin sometime in early November. I was born in Austin. I thought I would go to the courthouse and try to get info. Also I understand there is a birth book with all the births. Does anyone out there have advice for me? Or anything else I may need to do while I'm in Austin? I have my non-id info. I have contacted the home my mom was at. I was adopted at 3 days old. I was born April 30,1965. All advice is appreciated.