When you filed income taxes in LA, how did you do it? As a resident, or as a non-resident? On your return, did you note that you can be claimed as your parents' dependent? I don't know if it would come down to this, but you need to get all your ducks in a row in these cases, but if you filed as an LA resident and claimed an exemption for yourself, you are probably an LA resident...
Where are you registered to vote? The DL in LA ties you to LA.
Are you still in college, or just finishing? Or did you graduate and then not return to TX? If the latter, and you stayed in LA, had a job, etc, you are probably a LA resident.
I have no idea about splitting your residency in the 2 systems. Doesn't sound kosher, but maybe somebody else knows if there is any connection between the 2 systems...