After quite a bit of searching, I was finally able to find a clinic where I could get an appointment.
Nurse Practitioner Associates
210-610-2826
Everyone I have interacted with so far has been very friendly, and they were able to get me an appointment scheduled for today. The only drawback is they don't take insurance for HRT, so it's going to be an out of pocket expense of $200. It's a bit expensive, but I'm going to give it a try, and see how it goes.