There are many ways to help pay for doctor visits, even if you are undocumented. If you are pregnant, you can qualify for the CHIP program regardless of immigration status. Also, if you are undocumented but your children are US citizens, they can still be insured under CHIP.
The Gold Card only requires you to have proof of residency and proof of income. If you have documents of immigration status, you may include those in your application, but they are unnecessary. Even if you are undocumented and cannot find a program to help you get insurance, there are many places like Planned Parenthood which can provide some free basic care, such as treatment for STD’s or women’s health resources. A list of Planned Parenthood locations in the Houston area can be found here.