I have a south Texas accent. One of the cool things about Texas (and probably other places too) is the different accents all in the same state. Panhandle Texas accent is totally different from East Texas accent and totally different from south Texas accent.
I definitely have a southern drawl and a little Texas twang. It's more pronounced at times and I try hard to control it at other times. I totally say "y'all, all y'all, fixin' and drop the g on most words". I call it all Coke. Even if it's Sprite, it's Coke.
I think tv and movies accurately portray the TX accent. It differs so much from different areas of the state that they are depicting one somewhere in TX.
I've always wanted to have a Jersey accent. And be in the mob. Shhhhhh.