In Texas, do you have to actually sign a declaration of marriage to be married?

Texas Family code (which is the binding law but no the Texas Constitution) 2.401 provides the elements of proof of an informal marriage. If you agreed to be married, lived together as husband and wife in Texas, and represented to others that you were married, then you are married. If this woman has remarried without divorcing you, her second marriage is invalid. There's a burden of proof here, though - you have to prove each element - the initial agreement to marry and the representing to others that you are married ("holding out") has to be open and public - saying you are married sometimes and other times not might not cut it. And lastly, why would you care.

You don't have to sign a declaration of marriage to be married by common law in Texas. However, if she was already married to someone else, just cohabiting with you and holding herself out as married to you doesn't make her a bigamist. Likewise, cohabiting with the next guy doesn't make her a bigamist even if she's married to you by common law. You can't get married by common law if you're already married. Even if she married someone else formally after she split with you, you're very, very unlikely to get a prosecutor to charge her with bigamy. Your right to claim common law marriage will end two years after the split if you haven't filed for divorce by then.

Common law or informal marriage has 4 key elements but there is also a statute of limitations after the break up on how long you have to seek divorce. Regardless of whether you satisfy these 4 elements and the statute of limitations you would be unlikely to convince the local DA to prosecute her.