The type of foundation repair your home needs should be determined by a licensed structural engineer after a thorough investigation of the foundation failures. Foundation repair options can include using many methods. Much depends on where the foundation is cracking or sinking and by how much. It is a matter of the kind of soil under the house also.
If the house has a crawl space, then it is a good bet that the clay soil in the Houston area has dried out and the house support beams have lost their support because the soil has weakened too much. There may be many areas around the foundation where this is occurring.
The fix is to drive a pier down in the soil until it hits bedrock. This may be up to 20 feet, but the pier must rest on a hard ground surface. Once the pier is set by a hydraulic drive, then a series of steel plates are used to form a wedge between the top of the pier and the house foundation. It may be necessary to repeat this step several times around the foundation.
The beams that can be seen in the crawl space which support the house may be weakened or even cracked. The proper method for dealing with this condition is to use steel piers to lift the beam back into position and then attach another similar beam to the faulty beam by heavy screws.
The Ram Jack Procedure uses hydraulic pressure to drive steel column sections into the ground until they cannot go any further. Then a steel plate or plates are attached to the column and the house is raised by these plates using the hydraulic pressure used to drive the piles.
A slab on grade can sink in spots where the soil becomes soft from too much water, and then the soil dries out leaving a clay soil that will allow the foundation to move and crack. The best method is not to drill a hole in the slab if the slab is post tension construction. There are products that can be forced under the slab from the edge but near where the slab is cracked. By forcing this material under the slab, it will raise the slab where it is cracked and sinking.
The most important action to take is getting the sinking foundation fixed because it will cause serious problems.