Texas is one of the states that hasn't expanded Medicaid to cover every person who has a low income of a certain amount. That said, anyone can pay the premiums for another person's health insurance, which means that you can sponsor your sister by paying for her insurance premiums as a gift. There are also a lot of details that you didn't cover in your description of your sister's circumstances. You stated that your sister doesn't have an income. Medicaid is specifically designed for people with disabilities who don't have enough money to pay part or all of the cost of health insurance. Depending on the impact that your sister's epilepsy has on our life, she could qualify as disabled if she were to pursue that claim via the Social Security Administration. Rules are also changing all of the time in different states. Given her situation, she could still qualify for Medicaid at her age even without the federal designation.
The best course of action is to start over with Texas Health and Human Services to determine if your sister can qualify for Medicaid as long as a doctor is willing to state in writing that her epilepsy is a disability. Although you can help her apply for the benefits online on the Your Texas Benefits website, speak first with a social services caseworker at the closest benefits office in your sister's home county. YourTexasBenefits.com provides an office locator. Scroll down to the bottom of the page, select "Find an Office" and then follow the onscreen prompts. Since caseworkers can make mistakes and new ones have knowledge gaps, call a different local office and ask to speak with a manager about Medicaid if you've already spoken with a caseworker. If you meant that your sister does have an income, ask a social services representative about health coverage options for workers with disabilities. Even though again it sounds like your sister isn't classified as disabled at the federal level, she might still qualify at the state level depending on the rules at the time of the request.