Start by contacting your county office of the Texas A & M USDA Cooperative Extension Service and inquire about having a good, reliable soil test done so you know what your soils pH and base nutrient levels are so you can then work on creating a good, healthy soil to grow your grass in. Then dig in with these simple soil tests,
1) Structure. From that soil sample put enough of the rest to make a 4 inch level in a clear 1 quart jar, with a tight fitting lid. Fill that jar with water and replace the lid, tightly. Shake the jar vigorously and then let it stand for 24 hours. Your soil will settle out according to soil particle size and weight. A good loam will have about 1-3/4 inch (about 45%) of sand on the bottom. about 1 inch (about 25%) of silt next, about 1 inch (25%) of clay above that, and about 1/4 inch (about 5%) of organic matter on the top.

2) Drainage. Dig a hole 1 foot square and 1 foot deep and fill that with water. After that water drains away refill the hole with more water and time how long it takes that to drain away. Anything less than 2 hours and your soil drains too quickly and needs more organic matter to slow that drainage down. Anything over 6 hours and the soil drains too slowly and needs lots of organic matter to speed it up.

3) Tilth. Take a handful of your slightly damp soil and squeeze it tightly. When the pressure is released the soil should hold together in that clump, but when poked with a finger that clump should fall apart.

4) Smell. What does your soil smell like? A pleasant, rich earthy odor? Putrid, offensive, repugnant odor? The more organic matter in your soil the more active the soil bacteria will be and the nicer you soil will smell.

5) Life. How many earthworms per shovel full were there? 5 or more indicates a pretty healthy soil. Fewer than 5, according to the Natural Resources Conservation Service, indicates a soil that is not healthy.
and using what you find there as a guide work on improving the soil.
Then once you have good soil and the grass is growing well mow high and mulch mow to keep the level of organic matter in the soil at a good level. Water infrequently but deeply, when done watering the soil should be moist to at least a 4 inch depth and water when needed, no more.

I agree with the thought that it is all in the soil. The grass will grow well with very little additional fertilizers if the soil has good exchange sites for the nutirents to bond to and release.

This approach simplifies things greatly. Good soil structure can be formed by wetting and drying, or freezing and thawing.

I would add to the previous post that, besides watering only when necessary also, fertilize only when necessary. Remember that most organic sources are slow release to a large extent, so don't become to impatient.
Eventually you will be able to see what is needed when for a steady healthy feed.