I am currently residing in Louisiana, but work in Texas. All of my income in earned in Texas. They do not have state taxes. Do I have to pay Louisiana because that is where my primary residence is?

If you are resident of LA, yes you must report income on the LA tax return.
Your U.S. Tax Return: Working or Living in Two or More states (http://taxipay.blogspot.com/2008/06/working-in-two-or-more-states.html)