In Texas there are basically 3 ways to be "married". You can have a formal cerimonial marriage, you can have an "informal" marriage evidenced by a recorded "declaration of informal marriage" or you can be found by a Judge in a divorce action to have been "common law" married. Regardless of which way the marriage is created the rights and duties of the spouses are the same.
In regard to a "common law" marriage, that does NOT happen just because two people live together for any set period of time or even if they have a child together. The requirements for a court to find that there was a "common law" marriage are set out in Section 2.401 of the Texas Family Code and basically provide that the parties agreed to be married, lived together as husband and wife in Texas, and represented to others that they were married.
If you are in a realationship and are concerned about the rights and duties resulting from that, you need to talk to an attorney to go over the situation in detail and what the implications of your actions will be.