Is there a legal amount of time you have to live together in Texas for the common-law marriage to be valid?
No.
I am trying to see if I have a valid marriage, so I can determine if I should go through a divorce and have rights to alimony.
From your post, you ARE married and yes, you have to go through a formal divorce. As to whether you would be awarded spousal support or not.... the answer is no.
In Texas, absent abuse conviction, you must have been married for 10 years or more to qualify.
Texas Family Code:
"§ 8.051. ELIGIBILITY FOR MAINTENANCE; COURT ORDER. In a suit for dissolution of a marriage or in a proceeding for maintenance in a court with personal jurisdiction over both former spouses following the dissolution of their marriage by a court that lacked personal jurisdiction over an absent spouse, the court may order maintenance for either spouse only if:
(1) the spouse from whom maintenance is requested was convicted of or received deferred adjudication for a criminal offense that also constitutes an act of family violence under Title 4 and the offense occurred:
(A) within two years before the date on which a suit for dissolution of the marriage is filed; or
(B) while the suit is pending; or
(2) the duration of the marriage was 10 years or longer, the spouse seeking maintenance lacks sufficient property, including property distributed to the spouse under this code, to provide for the spouse's minimum reasonable needs, as limited by Section 8.054, and the spouse seeking maintenance:
(A) is unable to support himself or herself through appropriate employment because of an incapacitating physical or mental disability;
(B) is the custodian of a child of the marriage of any age who requires substantial care and personal supervision because a physical or mental disability makes it necessary, taking
into consideration the needs of the child, that the spouse not be employed outside the home; or
(C) clearly lacks earning ability in the labor market adequate to provide support for the spouse's minimum reasonable needs, as limited by Section 8.054."