Although I also live in Central Texas, I live far enough away from you weather may be different.
It's been so hot and humid where I live near Austin that it's been tough on my 3 mo. old pullets. The heat's been around 100 to 105 and the humidity varies, but it's been around 90% most of the day. Heat indexes have gone up to around 110, so I think that would be too much for any young critter to take right away.
I've been scared to put my new chicks out in it so they've been staying in an extra-large dog crate in the kitchen. I just used a "trouble light" and thermometer to keep the temp up in the right range for the first couple of weeks and a fan blowing on them if it got too hot in the kitchen. The outside chickens are getting lots of water, plenty of shade under the trees, a small fan, and I'll also water a small patch of soil so they can dig into that soil to lay down and cool off (like dogs do). I'm probably paranoid about it because my dog almost died of heat stroke and I've seen the high humidity drastically lowers her ability to combat the heat. I'd also heard of people in the general area losing birds to heat.
I hadn't tried the bottles of ice and I think I'll try that tomorrow for the bigger girls.