Hello Juliana,
Welcome to the ACA Forums!
Since you didn't provide much info, the answer I give may not be that accurate. Check out
https://forums.adventurecycling.org/index.php?topic=14587.0 for information that will provide a more accurate answer.
If you are heading to San Diego along ACA's Southern Tier Route (ST), I personally would not take US-83 between Brownsville and Laredo due to the volume of cars & trucks on the road. While it has a shoulder, to me, it would be no fun. I would head to San Isidro then to Hebbronville before heading to Laredo. From there, go Carrizo Springs > El Indio > Eagle Pass > Del Rio where you could connect to the ST (ACA has excellent map).
I would strongly suggest you head to Bend Ben Nat'l Park at Marathon then head west along the quiet FM-170 to Presidio before heading back north to Fort Davis to rejoin the Southern Tier to San Diego. You should note that the services can be quite far apart at times on this route.
If you are going to Austin, the scenery is not nearly as diverse but is much flatter and you will probably have a tailwind most of the way (unless a storm front is coming through). I have a route I have ridden going from Brownsville to Winnipeg. The route is primarily on low-traffic roads with services mostly available on a regular basis.
Of the two choices, I would do the ST Route as I it is longer and I like changes in the topography. You can contact me privately for some cue sheets and GPS data for the Austin Route. If doing this route, I highly suggest you have either a GPS or know who to download the GPS data to your phone and/or have an accurately calibrated bike computer to ensure you do not miss a turn.
Tailwinds, John