This is Joey.

I forgot to say that I am pulling a lot of the weeds up by hand. So many that my fingers have blisters!

Thanks, again.

Fertilizer added in dry years can stress turf if not irrigated and therefore aids the weeds, at least those that grow in the heat and drought, especially with extra nitrogen. How about some pix of the thorny weed?
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How much water are you delivering? If you are watering every day and the grass is not growing then it is not enough, your grass needs more water. Fertilizing grass that is in stress is never a good idea since that will only increase that stress and make conditions worse, especially if synthetic fertilizers are used.

Hi Gardendummie. Welcome to gardenweb. I know nothing about growing grass in TX, but wanted to say hi and suggest you might want to visit the lawn maintenance forum and/or TX forums.

I am watering every other day for 20 minutes in each station.

Can I fertilize again? I fertilized 3 weeks ago with a week and feed..

How much water is delivered in that 20 minutes? It is not the time that matters but the amount of water delivered. According to the, now retired, Director of Public Works here water pressure around 5:00 am is the lowest of the day because of the amount used as people are getting up and getting ready for the day so they system does not deliver the amount of water that would be delivered at 8:00 am.
When temperatures are consistently on the 80's and 90's your lawn may well need twice as much water as it would when the temperatures are in the 70's.
Is your water system delivering at least an inch of water per week? Is that inch per week really enough?

Does your St. Augustine go dormant in the winter where you live? If so, you probably shouldn't fertilize after Aug./September (depending on your growing season). Warm season grasses need to be allowed to STORE energy in the fall, not use it.