Above is the WSR-88D (NEXRAD) radar image from the Brownsville, TX (KBRO) site taken a few moments ago. You can clearly see the eye of Hurricane Alex about 30 miles East of the Mexican Coastline. This same position is about 96 miles South/Southeast of Brownsville, TX.
As of the 6pm Central Time National Hurricane Center Advisory, hurricane force winds extended out about 70 miles from the center of the storm. This means that hurricane force winds would impact land up to about 20 miles South of the Texas/Mexico border, on the present track. Tropical Storm force winds extend out from the center by just over 200 miles, and tropical storm force wind gusts have indeed been occurring across far South Texas during the last couple of hours.
So far for deep south Texas, very heavy rains have been the main story, along with some isolated wind damage reports:
The image below is the Brownsville radar estimate of storm total precipitaition thus far, through 6pm local time. The dark purple areas show rainfall estimates of 9-10 inches, while the lighter purple areas show rainfall estimates of 7-9 inches:
Widespread, sometimes heavy, rains will continue across far South Texas through much of the night and into Thursday. This will undoubtedly lead to flash flooding in many of the same areas.
Further North across central and the remainder of south Texas, rains have been tempered a bit today by the concentration of activity further South near the center of Alex. As the system moves inland tonight and tomorrow, additional moisture and energy is likely to flow Northeast into the remainder of the region, which will result in increasing rain chances there as well.