What Government or State Agency do I go to to see about getting paid for being a caregiver to both elderly parents?

You should not be paying any of your parents expenses. They should be eligible for programs that will assist them to pay for themselves and maybe a small stipend for you. You are working outside the home. None of your income is to be spent on them. What expenses do you pay for? Parents should be paying you through a care agreement and as an employee.

Contact your Area Agency on Aging.

https://www.agingcare.com/articles/how-to-get-paid-for-being-a-caregiver-135476.htm

https://www.agingcare.com/articles/10-government-programs-caregivers-can-access-for-their-elderly-parents-120513.htm

Always search this site for information about all things elderly. It is a wealth of information.

Do they have medicaid?

I’m sorry you are having such a difficult time.
Here is the link to your local Area Agency on Aging. I encourage you to contact them for a needs assessment for your parents and any help they have for caregivers.

https://hotcog.org/health-and-human-services-programs/area-agency-on-aging/

You should be asking your parents to compensate you. If they are low income and medically qualified then they may be eligible for a state program that may pay you but the pay is low. You can contact your area on aging or the Texas health and human services office to find out what’s available in your area & how your parents can apply.