Hays County received a shipment of 1,950 Pfizer COVID-19 vaccine doses and opened an appointments portal on January 22. Within about 25 minutes of the portal opening, all appointment slots were filled.  See this page for details:
https://hayscountytx.com/2021/01/22/covid-19-vaccine-appointments/

For updates check the Hays County website for new announcements.
Hays County | The official website of the government of Hays County, Texas (hayscountytx.com)

You may also look to the Hays County Health Department for updates:
Local Health Department | Hays County (hayscountytx.com)

The appointments portal is at this link, but it might change.  So check the other Hays sites to be sure.
COVID-19 | Haysinformed​​​​​​​