If the U.S. immigration services determine you are not eligible to come into the country, you may not be able to move here and make Texas your home. However, you may also qualify for an exemption to your inadmissibility. Do keep in mind such exceptions are not given freely. You will have to meet strict requirements. The specific waiver you may be able to get is based on the extreme hardship policy.
The U.S. Citizenship and Immigration Services admits that there is no one firm definition of what qualifies as an extreme hardship. This complicates things. However, the idea behind this waiver is to prevent cases of unusual hardship for U.S. citizens who have a family member who is not allowed entry to the U.S.
The key here is that the hardship has to be something beyond normal. So, for example, saying the hardship would be monetary only would probably not qualify as extreme because that is a very normal occurrence. You would need something that is unusual and not common. It is very normal for every single family who has a member denied entry to experience some hardship because of the denial. Extreme hardship goes further than that.
The final say really lies with the court. The Supreme Court has weighed in and remains rather vague in letting the agencies handle defining what is and what is not an extreme hardship. So, immigration courts have to make the determination, and the standards there are set very high. This information is for education and is not legal advice.