I scheduled my K1 Visa interview in June 2nd 2021 for July 9th.
I immediately called UC CHRISTUS's call center to ask about scheduling an appointment, and they told me the main panel physician Dr. Moore did not have any appointments available until August. They gave me her work email and told me to contact her.
After reaching out to the email, in a week they managed to create a "sobrecupo" or special appointment for June 23. They were very clear about what to bring to the medical appointment: documents printed, a big envelope, your vaccination history and several pictures.