If you are going to do that, you will need to leave by early tomorrow morning - early as in 4 am or so.
And realize - there are NO HOTELS anywhere to be found until you get to Oklahoma or New Mexico - and the storm is going to be tracking north through the Dallas metroplex and up into Oklahoma.
I called as far west as Midland and Fort Stockton and all the hotels were booked.
Lots of churches, Salvation Army, RC, and some civic groups have booked blocks of hotel rooms. Anybody in the evac zone should not wait. West to San Antonio may be a good bet. Yhe RC has info tents set up on the evac routes. There are signs directing people to the info centers and shelters.